Shear Mechanisms in Fabric-Reinforced Cementitious Matrix Overlays: Experimental and Numerical Investigation

Acknowledgments

Notation

A

positive coefficient ruling the distance of the vertex of the hyperbola;

A_f

area of the FRCM effective in shear;

B

positive parameter calibrating the opening of the hyperbola;

Cⁱ

isotropic elastic matrix of the ith material;

D

interface damage;

D_c

damage variable in compression;

D_t

damage variable in tension;

d

spacing between yarns;

E

elastic modulus of the mortar;

E_cm

average Young’s modulus of the mortar;

E_tm

average tensile elastic modulus of the fabric;

${\overline{e}}_{eq}$

nonlocal equivalent elastic strain;

e₀

limit elastic strain in tension;

e₁;e₂

principal elastic strains;

f_b

FRCM bond strength;

f_cm

average compressive strength of the mortar;

f_f

design tensile strength of FRCM;

f_sm

average tensile strength of the mortar;

f_t

fabric tensile strength;

f_tm

average tensile strength of the fabric;

f_Y

yield function;

G

shear modulus of elasticity;

G₁₂

in-plane elastic shear modulus of the fabric;

g_L

gauge length;

H_w

height of the wall;

K

diagonal stiffness matrix;

k

evolution of the tensile damage function parameter;

L_w

width of the wall;

m_d

fabric mass density;

N

number of specimens tested;

n

number of FRCM-reinforced sides of the wall;

P

load recorded by the load cell of the testing machine;

p

plastic part of the strain;

$\dot{\mathit{p}}$

evolution law of the plastic strain;

R_c,t

nonlocal radius;

s

relative displacement;

s_fh

spacing of the horizontal FRCM strips;

s_u

full damage relative displacement;

s₀

damage threshold;

t_s

thickness of the specimen;

t_f

equivalent thickness of the fabric;

t_fh

equivalent thickness of the horizontal FRCM reinforcement;

u_v

vertical displacement;

V_f

increase of the shear strength of a masonry wall provided by FRCM;

V_uw

ultimate shear load per unit width;

w

dimension of specimen side;

w_fh

width of the horizontal FRCM strips;

ΔH

horizontal shortening of the specimen;

ΔV

vertical extension of the specimen;

ɛ

total strain;

ɛ_u

ultimate compressive strain of mortar;

ɛ_v

vertical tensile strain;

ɛ_Y

strain corresponding to the peak stress;

γ

shear strain;

η

trace of the elastic strain;

η_f

coefficient related to the strengthening configuration;

Γ_c

energy dissipated in uniaxial compression;

Γ_t

tensile damage energy;

κ

accumulated plastic strain;

$\overline{\kappa }$

nonlocal accumulated plastic strain;

κ_u

accumulated plastic strain associated with the full compressive damage;

$\dot{\lambda }$

plastic multiplier;

$\dot{\mathit{p}}$

plastic strain increment;

σ

stress;

$\overline{\mathit{\sigma }}$

effective stress;

σ_Y

compressive strength;

Σ

in-plane interfaces to simulate slippage of the fiber layer within the mortar;

Σ_TIE

rigid link;

τ

shear stress;

Ψ_c

compressive weight functions;

Ψ_t

tensile weight functions;

Ω_f

textile inner layer in the numerical modeling;

Ω_m

mortar outer layers in the numerical modeling; and

Ω_s

steel plate in the numerical modeling.

References