Experimental and Analytical Study on Precast High-Strength Concrete Tunnel Lining Segments Reinforced with GFRP Bars

Acknowledgments

Notation

A_f

area of longitudinal reinforcement in the bottom mesh (mm²);

$A_f^{\mathrm{\prime }}$

area of longitudinal reinforcement in the top mesh (mm²);

b

width of a section (mm);

b_w

effective width of a section (mm);

c

neutral-axis depth (mm);

d

effective depth of a section (mm);

d′

distance between the centroid of longitudinal reinforcement in the top mesh to the extreme compression fiber (mm);

E_c

concrete modulus of elasticity (MPa);

E_c,HSC

high-strength concrete modulus of elasticity (MPa);

E_el

elastic energy (J);

E_f

FRP reinforcement modulus of elasticity (MPa);

E_tot

total absorbed energy at ultimate load (J);

E_{ψ = 0.005/d}

absorbed energy until the curvature of 0.005/d, where d is the effective sectional depth in mm (J);

$f_c^{\mathrm{\prime }}$

concrete compressive strength (MPa);

f_cr

concrete tensile strength (MPa);

f_f

stress in the bottom FRP reinforcement in tension (MPa);

$f_f^{\mathrm{\prime }}$

stress in the top FRP reinforcement in tension (MPa);

h

depth of section (mm);

J

deformability factor;

J_VG

curvature-based deformability index;

k

ratio of neutral-axis depth to reinforcement depth;

k_n

ratio of neutral-axis depth to reinforcement depth considering the axial-load level;

L

span between reaction forces acting on the centerline in the test setup (mm);

l

clear-span length in calculating the deflection (mm);

l_n

parameter to account for the effect of the section width, effective depth, concrete compressive strain, and concrete modulus of elasticity in calculating k_a (N);

M

bending moment induced in the tunnel segment specimens during the test (N · mm);

$M{}_c$

moment at a concrete strain of 0.001 (N · mm);

M_ultimate

ultimate moment (N · mm);

N

axial load induced in the tunnel segment specimens during the test (N);

n_f

ratio of the modulus of elasticity of the longitudinal FRP bars to the modulus of elasticity of the concrete;

P

amount of axial load (positive for tension and negative for compression) (N);

R

reaction force from the supports (N);

V

shear force induced in the tunnel segment specimens during the test (N);

V_c

shear capacity provided by concrete (N);

α₁

ratio of the average stress of the equivalent rectangular stress block to $f_c^{\mathrm{\prime }}$;

β₁

ratio of the depth of the equivalent rectangular stress block to the neutral-axis depth;

Δ

vertical distance from the center of the specimen to the point at which the reaction forces are applied in the test setup (mm);

ɛ_c

concrete compressive strain;

ɛ_cu

ultimate concrete compressive strain;

θ

inclination angle of the reaction forces in the test setup (rad);

μ_e

energy-based ductility index;

ξ

time-depended factor for sustained load;

ρ_f

longitudinal reinforcement ratio;

Ψ_c

curvature at a concrete strain of 0.001 (1/mm); and

Ψ_ultimate

ultimate curvature (1/mm).

References