Stress Reduction Coefficient and Amplification Factor for Seismic Response of Ground

Incorporating the increase of shear modulus with depth $\left(z\right)$ by using a depth exponent $p$ , the response of linear visco-elastic ground under steady state harmonic vibration was examined. The soil mass lying above the rigid base was discretized into a large number of horizontal layers. For a given vertical thickness $\left(H_r\right)$ of the upper ground material in the first mode of resonance, it was noted that the resonant frequency $\left(f_r\right)$ as well as the values of amplification factor $\left(M_f\right)$ and the stress reduction coefficient $\left(C_d\right)$ at a given $z∕H_r$ can be computed as a function of $p$ and $D$ , where $D$ is the damping ratio of the material. An increase in $D$ leads to (1) an increase in $C_d$ ; (2) a very little increase in $f_r$ ; and (3) a decrease in $M_f$ . On the other hand, an increase in $p$ causes: (1) an increase in $f_r$ ; (2) a marginal increase in $M_f$ ; and (3) a decrease in $C_d$ . It was evident that the values of $M_f$ and $C_d$ at a given depth will be affected significantly by changes in the chosen thickness of the soil deposit in resonance.