GFRP Composite Culverts for Hydraulic and Agricultural Underpasses: Structural Behavior, Design, and Application

Acknowledgments

Notation

A

sectional area;

c_ref

cohesion of soil;

d₁

vertical displacement at midspan;

d₂

horizontal displacement at the left-hand side;

d₃

horizontal displacement at the right-hand side;

d₄

vertical displacement at the invert;

E

instantaneous elastic modulus;

E_c,L

longitudinal compressive elastic modulus;

E_c,T

transverse compressive elastic modulus;

E_d

design combination of actions;

E_f,L

longitudinal flexural elastic modulus;

E_fr

frequent combination of actions;

E_ref

elastic modulus of the soil;

E(t)

long-term (at time t) creep elastic modulus;

e₁

top strain in the vicinity of midspan;

e₂

bottom strain in the vicinity of midspan;

F

applied load;

G_k

permanent loads;

L

transverse span of the culvert;

M

bending moment;

M_max

maximum bending moment;

N

axial force;

N_max

maximum axial force;

Q_k

leading road traffic action;

Q_1k

tandem system load (Load Model 1);

q_1k

uniformly distributed load (Load Model 1);

R_d

design resistance;

S_c,L

longitudinal compressive strength;

$S_{c,L,k}^{}$

longitudinal compressive characteristic strength;

S_c,T

transverse compressive strength;

S_f,L

longitudinal flexural strength;

$S_{f,L,k}^{}$

longitudinal flexural characteristic strength;

S_f,T

transverse flexural strength;

S_il,L

longitudinal interlaminar strength;

$S_{il,L,k}^{}$

longitudinal interlaminar characteristic strength;

S_il,T

transverse interlaminar strength;

T_g

glass transition temperature;

t

time;

V

shear force;

V_max

maximum shear force;

W

elastic section modulus;

${\delta }_{G,k}^{}$

instantaneous deflections due to permanent loads;

${\delta }_{G,k}^{\mathrm{long}-\mathrm{term}}$

long-term deflections due to permanent loads;

${\delta }_{Q,fr}^{}$

deflections due to frequent road traffic loads;

δ_Q,1k

deflections due to tandem-system characteristic loads (Q_1k);

${\delta }_{fr}^{}$

short-term deflections due to the frequent combination of actions;

${\delta }_{fr}^{\mathrm{long}-\mathrm{term}}$

long-term deflections due to the frequent combination of actions;

δ_q,1k

deflections due to uniformly distributed characteristic load (q_1k);

δ_max

maximum deflection;

${\epsilon }_{11}^{}$

longitudinal strain;

${\epsilon }_{22}^{}$

transverse strain;

γ

specific weight of the soil;

γ_G

permanent load partial factor;

γ_Q

variable load partial factor;

γ_Rd

resistance model partial factor;

γ_m

material partial factor;

η_c

overall conversion factor;

η_cm

moisture conversion factor;

η_ct

temperature conversion factor;

σ₁₁

longitudinal stress (compressive or flexural);

σ₂₂

transverse compressive stress;

σ₁₃

longitudinal interlaminar stress;

σ₂₃

transverse interlaminar stress;

σ⁺

tensile axial stress;

σ⁻

compressive axial stress;

τ

shear stress;

φ

angle of internal friction of the soil; and

ϕ_E(t)

creep coefficient at time t.

References