Seismic Response of a Rockfill Dam with an Asphalt–Concrete Core under P Waves with Arbitrary Incident Angles

Data Availability Statement

Notation

A

correction coefficient of the stiffness coefficient;

A_b

affected area of the boundary node;

A₁

amplitude ratio of the reflected P wave to the incident P wave;

A₂

amplitude ratio of the reflected SV wave to the incident P wave;

a_max

seismic peak ground acceleration;

a(t)

stationary Gaussian stochastic process;

B

correction coefficient of the damping coefficient;

C_k

amplitude of the kth frequency;

c_P

velocity of the P wave;

c_S

velocity of the S wave;

D

damping ratio;

D_max

maximum damping ratio;

${\mathbf{F}}_B^{ff}$

equivalent nodal load;

f(t)

strength envelope;

G

shear modulus;

H

height of the foundation;

K_e

seismic safety factor;

k₁

dynamic shear modulus coefficient;

L_x

x-direction length of the foundation;

L_z

z-direction length of the foundation;

p

probability;

R

distance from the scattering source to the truncated boundary of the foundation;

S(ω_k)

power spectral density function;

S_a,T(ω_k)

target acceleration response spectrum;

T_d

total duration of the random process;

T_g

site excellence period;

t₁

first moment of the control stationary section;

t₂

last moments of the control stationary section;

t₃

duration of the ground motion;

${\mathbf{u}}_B^{ff}$

displacement vector;

${\dot{\mathbf{u}}}_B^{ff}$

velocity vector;

u₀(t)

incident displacement time history;

α

oblique incident angle;

β

SV wave with the reflection angle;

β_max

maximum value of the standard response spectrum;

β(T)

standard response spectrum;

Δt₁

time delay of the incident P wave;

Δt₂

time delay of the reflected P wave;

Δt₃

time delay of the reflected SV wave;

γ

incident direction angle;

${\overline{\gamma }}_d$

reference shear strain;

λ

lame constant;

ρ

mass density;

${\sigma }_B^{ff}$

stress tensor;

τ

total shear stress;

τ_f

shear strength;

ω_k

circle frequency of the kth frequency;

φ_k

uniformly distributed random phase angle;

ζ

attenuation coefficient; and

ξ

attenuation constant.

References