Seismic Bearing Capacity of Geosynthetic Reinforced Strip Footings Using Upper Bound Limit Analysis

Acknowledgments

Notation

a, b

regression coefficients;

B

foundation width;

c

soil cohesion;

d

embedment depth of reinforcement layer;

$\dot{D}$

rate of internal work by the reinforcement;

f_b

coefficient of interface friction;

f_c

coefficient of interface adhesion;

k_h

horizontal pseudostatic seismic coefficient;

l

reinforcement length;

L_BE

length of surcharge zone;

l_e,i

reinforcement effective length in the ith block;

n

number of blocks in the multiwedge mechanism;

N_c

bearing capacity coefficient for the contribution of cohesion;

N_e

number of wedges through which reinforcement extends;

N_q

bearing capacity coefficient for the contribution of surcharge;

N_t

bearing capacity coefficient for the contribution of reinforcement;

N_γ

bearing capacity coefficient for the contribution of unit weight;

N_γE

equivalent bearing capacity coefficient;

q_f

surcharge pressure;

Q_f

surcharge load;

q_u

ultimate bearing capacity of foundation;

Q_u

ultimate load of foundation;

q_uo

unreinforced soil bearing capacity;

T_t

reinforcement tensile strength per unit width of reinforcement;

V_F

magnitude of velocity vector corresponding to zero horizontal velocity jump;

V_i

velocity of the ith block;

V*

total horizontal velocity jump for the reinforcement;

W_i

weight of the ith block;

α_i, β_i

interior angles of the ith block;

γ

soil unit weight;

$⟨\stackrel{\cdot }{{\epsilon }_l}⟩$

strain rate;

θ

angle between reinforcement and direction of the velocity jump vector;

[v]

magnitude of the velocity jump vector across the failure surface;

v_l,i

relative reinforcement-soil velocity in the ith block;

σ_n

normal stress; and

φ

soil friction angle.

References