Physical Properties and Durability of Green Fiber-Reinforced Concrete for Road Bridges

2.1 Calculation of crack resistance

The Code for Design of Concrete Structures (GB 50010-2010) gives the calculation formulas for crack control under extreme conditions for the reinforced concrete, prestressed concrete, and plain concrete suitable for houses and general structures during normal use. Let ω_F be the crack resistance enhancement coefficient (CREC) of fibers of RBGFRC. Then, the relevant parameters can be adjusted by the said formulas. Let β denote the partial coefficient of concrete strength; e denote the beam section width; a denote the height of the compressive zone of concrete; g_s denote the designed axial compressive strength concrete; g_b^* and g_b denote the designed compressive and tensile strengths of rebar, respectively; S_c^* and S_c be the section area of compressed and tensioned rebar, respectively. Then, we have:

${{\beta }_{1}}{{g}_{s}}ea+g_{b}^{*}S_{c}^{*}={{g}_{b}}{{S}_{c}}$      (1)

Let d₀ be the effective height of road bridge; l be the distance from the point of composite compression on the rebar to the pressure boundary of rebar section. Then, the bending moment capacity of normal section CB_ho can be calculated by:

$C{{B}_{ho}}={{\beta }_{1}}{{g}_{s}}ea\left( {{d}_{0}}-\frac{a}{2} \right)+g_{b}^{*}S_{c}^{*}\left( {{d}_{0}}-l \right)$      (2)

Let W_ho be the crack load of original concrete road bridge. Then, the bending moment capacity of normal section CB_ho of original concrete road bridge can be calculated by:

$C{{B}_{ho}}=\frac{{{W}_{ho}}}{2}\times 0.36$      (3)

After determining the relevant parameters, it can be calculated that the W_ho belongs to 65-70kN, when the CB_ho of original concrete varies within 11-12kN·m.

Based on the provisions on the mix ratio of recycled aggregate in the Code for Design of Concrete Structures (DB11/T 803-2011), the relevant formulas on the carrying capacity of road bridge concrete mixed with 50% green fiber aggregate should be multiplied with a reduction coefficient of 70%. Then, the ultimate load W_ho falls in 45-50kN. The value of ω_F depends on the crack load W_dl and maximum crack width θ_max of green fibers.

Referring to the empirical formula on crack load in Chinese national standards and codes, the crack load W_dl of the concrete road bridge before mixing green fibers in actual conditions can be calculated by:

${{W}_{dl}}=\frac{{{W}_{ho}}}{3}$     (4)

Through actual tests on concrete road bridges before mixing green fibers, the measured crack load W_dl fell within 18-20kN, about 1/5 greater than theoretical calculation. It can be proved that theoretical crack load of RBGFRC is smaller than the actual value. For the crack safety of RBGFRC, the CREC ω_F of fibers was fitted and adjusted by reducing the actual crack load of the road bridge by 1/4. Table 1 presents the ω_F values calculated based on W_ho.

Table 1. ω_F values calculated based on W_ho

The crack load of concrete road bridges mixed with different types of green fibers can be calculated by similar methods. Comparing the actual crack load with calculated crack load, it is possible to obtain the crack resistance adjustment coefficient of the current type of RBGFRC, that is, the CREC ω_F of fibers. To calculate the CREC ω_F of fibers at different mix ratios, the relevant codes specify that the formulas on the carrying capacity of road bridge concrete mixed with 50% green fiber aggregate should be multiplied with a reduction coefficient of 70%. Based on the calculated ω_F, the crack load of a fixed type of RBGFRC can be calculated by:

$W_{O-h o}=70 \% \times \omega_{F} \times W_{d l}$      (5)

Another important indicator of the crack resistance of RBGFRC is the maximum crack width. Let σ_R be crack expansion coefficient; Φ, M_C, and τ_C be the stress nonuniformity coefficient, elastic modulus, and equivalent diameter of rebar, respectively; CB_S be the bending moment calculated by standard combinations; d₁ be the effective section height; γ be the empirical coefficient characterizing the type of force component; ε be the thickness of road bridge protective layer; η_RB be the effective reinforcement rate, which equals the ratio of longitudinally tensioned rebar area S_C to the section area of tensioned concrete S_RB: η_RB=S_C/S_RB. Then, the maximum crack width θ_max can be calculated by:

${{\theta }_{max}}=0.83{{\sigma }_{R}}\Phi \frac{{{\xi }_{RE}}}{{{M}_{C}}}\gamma \left( 1.8\varepsilon +0.69\frac{{{\tau }_{C}}}{{{\eta }_{RB}}} \right)$     (6)

${{\xi }_{RE}}=\frac{C{{B}_{S}}}{0.86{{d}_{1}}{{S}_{C}}}$     (7)

The maximum crack width of concrete road bridges mixed with different types of green fibers can be calculated by similar methods. The relevant codes specify that the formulas on the maximum crack width of road bridge concrete mixed with 50% green fiber aggregate should be multiplied with an amplification coefficient of 1.44. Then, the maximum crack width of a fixed type of RBGFRC can be calculated by:

${{\theta }_{O}}=1.44\times {{\omega }_{H}}\times {{\theta }_{max}}$     (8)

Table 2 presents the ω_F values calculated based on θ_max.

Table 2. ω_F values calculated based on θ_max

2.2 Calculation of shear capacity of oblique section

The Code for Design of Concrete Structures (GB 50010-2010) gives the calculation formulas for the shear capacity of oblique section under extreme conditions. Let ω_S be the shear capacity enhancement coefficient (SCEC) of fibers of RBGFRC. Then, the following part will discuss about the adjustment coefficient for computing the oblique section capacity of road bridges reinforced with green fibers. Let F_S and g_h be the shearing resistance and shear capacity of the concrete in the shear zone, respectively; F_BT and F_BU be the shearing resistances of stirrup and bend bar, respectively. Then, the shear capacity F_OS of the oblique section of road bridge can be calculated by:

_{${{F}_{OS}}={{F}_{S}}+{{F}_{BT}}+{{F}_{BU}}$      (9)}

Formula (9) shows that the calculation of shear capacity of oblique section is premised on the accurate computing of the shear failure force F_OB on the oblique section of road bridge. Let η_BT and g_BT be the effective reinforcement rate and shear capacity of stirrup, respectively. Then, the shear failure force F_OB of road bridge without bend bar can contain F_S and F_BT:

${{F}_{OB}}={{F}_{S}}+{{F}_{BT}}$      (10)

$\frac{{{F}_{OB}}}{{{g}_{h}}e{{d}_{1}}}=0.68+1.23{{\eta }_{BT}}\frac{{{g}_{BT}}}{{{g}_{h}}}$     (11)

Let S_BT be the section area of stirrup. Then, formulas (10) and (11) can be converted into the form under ultimate state:

$F\le {{F}_{OB}}=0.68{{g}_{h}}e{{d}_{1}}+1.23{{g}_{BT}}\frac{{{S}_{BT}}}{C}{{d}_{1}}$     (12)

Let μ be shear span ratio; l_STS be the distance from the oblique section of bridge to the bearing section or node boundary. Then, we have μ=l_STS/d₁, with μ belonging to [1.47, 3.01]. Taking rectangular beam, T-beam, and H-beam for example, the F_OB of road bridge mainly under concentrated load can be calculated by:

$F\le {{F}_{OB}}=\frac{1.75}{\mu +1.0}{{g}_{h}}e{{d}_{\text{1}}}+{{g}_{BT}}\frac{{{S}_{BT}}}{C}{{d}_{1}}$      (13)

For road bridge with stirrup and bend rebar, the shear capacity is the superposition between shear failure force F_OB and shearing resistance of bend rebar F_BU:

_{${{F}_{OS}}={{F}_{OB}}+{{F}_{BU}}$     (14)}

Then, the stress nonuniformity coefficient was set to 0.76. Let $\delta$ be the angle between the bend rebar and the longitudinal axis of the beam; S_BU be the section area of the bend rebar. Then, the shearing resistance of the bend rebar can be calculated by:

${{F}_{BU}}=0.\text{76}{{g}_{b}}{{S}_{BU}}sin\delta $     (15)

Under normal circumstances, the shear capacity of the bending component on the oblique section of road bridges with rectangular beam, T-beam, and H-beam satisfies:

$\begin{align}  & F\le 0.68{{g}_{h}}e{{d}_{1}}+1.23\frac{{{S}_{BT}}}{C}{{g}_{BT}}{{h}_{1}} \\ & +0.76{{S}_{BU}}{{g}_{b}}\sin \delta  \\\end{align}$    (16)

Under special circumstances, a road bridge under concentrated load satisfies:

$\begin{align}  & F\le \frac{1.75}{\mu +1.0}{{g}_{h}}e{{d}_{\text{1}}}+\frac{{{S}_{BT}}}{C}{{g}_{BT}}{{d}_{1}} \\ & +0.76{{S}_{BU}}{{g}_{b}}\sin \delta  \\\end{align}$     (17)

To prevent the road bridge from being damaged by the oblique pressure, it is necessary to define the upper limit of maximum reinforcement rate and the lower limit of the minimum section area. Let ϕ_HS be the concrete strength influence coefficient. The ϕ_HS value is 1 and 0.8 when the concrete strength is smaller or equal to C50 and C80, respectively. When the concrete strength falls between the two grades, the ϕ_HS value can be determined through linear interpolation. Then, a general road bridge with an effective height of d_G satisfies:

$\frac{{{d}_{G}}}{e}\le 4,F\le 0.2\text{3}{{\delta }_{HS}}{{g}_{HS}}e{{d}_{1}}$    (18)

A thin webbed beam road bridge with an effective height of d_TW satisfies:

$\frac{{{d}_{TW}}}{e}\le 6,F\le 0.2{{\delta }_{HS}}{{g}_{HS}}e{{d}_{1}}$      (19)

A road bridge of any other tye with an effective height of d_O satisfies:

$4<\frac{{{d}_{O}}}{e}<6,F\le 0.027\left( 16-\frac{{{d}_{O}}}{e} \right){{\alpha }_{HS}}{{g}_{HS}}e{{d}_{1}}$     (20)

The next step is to define the lower limit of minimum reinforcement rate and stirrup reinforcement condition. Ignoring stirrup reinforcement, we have:

$F\le 0.\text{68}{{g}_{h}}e{{d}_{\text{1}}}$     (21)

Under normal circumstances, a road bridge not under concentrated load satisfies:

$F\le \frac{1.75}{\mu +1.0}{{g}_{h}}e{{d}_{\text{1}}}$     (22)

Under special circumstances, when F>0.68g_hed₁, the minimum reinforcement rate of a road bridge under concentrated load satisfies:

$\eta \ge {{\eta }_{c,min}}={{\left( \frac{{{S}_{BT}}}{eC} \right)}_{min}}=0.25\frac{{{g}_{h}}}{{{g}_{BT}}}$    (23)

Table 3 presents the calculation results of ω_S.

Table 3. Calculated results on ω_S

After determining the relevant parameters of road bridges, it can be calculated that the μ value of original concrete belongs to 1.9-2, indicating that the concrete is of grade C30. The corresponding g_h value falls in 1.4-1.5N/mm². Further, the shear capacity F_OS can be limited to the range of 36-40kN. After being multiplied with the reduction coefficient, the value range was narrowed down to 26-30kN. It can be proved that the theoretical shear capacity of RBGFRC is smaller than the actual value. For the shear safety of RBGFRC, the SREC ω_S of fibers was fitted and adjusted by reducing the measured shear force of the road bridge by 1/5. The shear capacity of the road bridge reinforced with a fixed type of green fibers can be calculated by:

$F_{O-O S}=70 \% \times \omega_{S} \times F_{O S}$     (24)

2.3 Calculation of bending capacity of normal section

The Code for Design of Concrete Structures (GB 50010-2010) gives the calculation formulas for the bending capacity of oblique section under extreme conditions. For RBGFRC with planar sections, it is assumed that the green fibers have a good bonding effect and an obvious synergy, and the concrete spalling is so small as to be negligible. Without considering the tensile strength of concrete and the effect of green fibers on bending capacity, the authors explored the adjustment parameter, i.e., the bending capacity reinforcement coefficient (BCRC), of green fibers for computing the bending capacity of normal section of the road bridge reinforced with green fibers. The bending capacity of normal section of original road bridge can be obtained by substituting the value range of the ultimate load W_ho in the previous subsection into the following formula:

$C{{B}_{OS}}=\frac{{{W}_{ho}}}{2}\times 0.35$    (25)

The ultimate load W_ho of RBGFRC is slightly higher than the theoretical value. For the bending safety of RBGFRC, the BREC ω_B of fibers was fitted and adjusted by reducing the measured ultimate load force of the road bridge by 30%. Let ω_OS be the calculated bending moment capacity of normal section of the road bridge reinforced by green fibers can be calculated by:

$C B=70 \% \times \omega_{O S} \times C B_{O S}$   (26)

Table 4 presents the calculation results of ω_B.

Table 4. Calculated results on ω_B

Through experiments, the RBGFRC durability was analyzed from three aspects: carbonation resistance, resistance to freeze-thaw cycles, and porosity.

Table 9. Carbonation data of RBGFRC

The calcium hydroxide generated through cement hydration reacts with the carbon dioxide in the air, leading to the carbonation of concrete. This directly brings down the alkalinity of road bridge concrete. The ensuing corrosion of internal rebars will further damage the bridge structure.

Table 9 presents the carbonation data of RBGFRCs with different fiber dosages after being cured for 8 days, and 30 days, respectively. Figure 5 shows the influence of green fiber dosage on the carbonation depth strength of the road bridges made of these RBGFRCs.

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Figure 5. Influence on carbonation depth

Table 10. Relative dynamic moduli of RBGFRC

After being cured for 8 and 30 days, the minimum carbonation depths of the concrete both appeared at the fiber dosage of 0.06%. As the dosage changed from 0.18% to 0.42%, the carbonation depth did not fluctuate obviously. Thus, the carbonation resistance of road bridge concrete slightly drops with the increase in green fiber dosage.

The carbonation resistance of the concrete peaks at the dosage of 0.06%, mainly because the internal pores are filled up by the calcium carbonate produced by the carbonation of the randomly distributed fibers, making the concrete more stable under carbonation. However, with the growth of fiber dosage, intercommunicating holes will appear on the weak bonding interface between green fibers and concrete, which increases the carbonation depth.

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Figure 6. Influence on relative dynamic modulus

Table 10 lists the relative dynamic moduli of concretes enhanced by different dosages of green fibers through 0-50 freeze-thaw cycles. Figure 6 shows the influence of green fiber dosage on the relative dynamic modulus of the road bridges made of these RBGFRCs.

Before the 35^th cycle, the RBGFRCs mixed with different dosages of green fibers differed slightly in relative dynamic modulus; After that cycle, the difference gradually increased with the freeze-thaw cycles. It can be proved that RBGFRC has better resistance to freeze-thaw cycles than the original concrete.

The rising resistance to freeze-thaw cycles is attributable to the fact that the bridge structure is densified as the randomly distributed green fibers fill the internal pores of the concrete, which reduces the stress difference created by the alternation between positive and negative temperatures.

Table 11. Mass loss rates

Table 11 lists the mass loss rates of concretes mixed with different dosages of green fibers through 0 to 50 freeze-thaw cycles. Figure 7 shows the influence of green fiber dosage on the mass loss rate of the road bridges made of these RBGFRCs through 0 to 100 cycles.

The mass loss rate of the road bridge did not change much within 50 cycles, and increased at a growing rate after the 50^th cycle. The addition of green fibers greatly reduced the mass rate of the concrete. The RBGFRC had much better resistance to freeze-thaw cycles than ordinary concrete.

The superiority mainly comes from the stacking between the randomly distributed green fibers, which enhances the bonding effect of concrete, making the concrete more stable through resistance to freeze-thaw cycles.

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Figure 7. Influence on mass loss rate

Table 12. Total porosity of RBGFRC

To represent the pore structure of road bridge concrete more intuitively, Table 12 presents the total porosity of concretes mixed with different dosages of green fibers. Figure 8 offers the influence of green fiber dosage on pore distribution of concrete road bridge.

Obviously, the addition of green fibers clearly suppresses the total porosity of concrete. The total porosity minimized at 13.98 at the dosage of 0.48%. The main reason is that green fibers make up the pores, making the concrete denser and more durable.

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Figure 8. Influence on total porosity