SEISMIC ANALYSIS Stability of a slope can be affected by seismicity in two ways: earthquake and blasting. These seismic motions are capable of inducing large destabilizing inertial forces. • Pseudostatic Method: The earthquake’s inertial forces are simulated by the inclusion of static horizontal and vertical forces in limit equilibrium analysis. • Newmark’s Diaplacement Method: This method is based on the concept that the actual slope accelerations may exceed the static yield acceleration at the expense of generating permanent displacements (Newmark, 1965). • Dynamic Finite Element Analysis: This is a coupled two or three dimensional analyses using appropriate constitutive material model that will provide details of concerning stresses, strains, and permanent displacement. Types of seismic wave The main seismic wave types are • Compression (P) • Shear (S) • Rayleigh (R) • Love (L) P and S waves are known as body waves, because they propagate outward in all directions from source (such as an earthquake) and travel through the interior of the earth. Love and Rayleigh waves are surface waves and propagate approximately parallel to the earth’s surface. Typical seismogram ( www.geo.mtu.edu) definition of earthquake terms (www.culcanhammer.net) Dynamic Soil Properties Important elements in a seismic response analysis are: input motions, site profile, static soil properties, dynamic soil properties, constitutive models of soil response to loading and methods of analysis using computer programs. Simulation of seismic effect there are two basic approaches to incorporate the seismic effect on slope stability Inertia slope stability analysis weakening slope stability analysis Pseudo-static approach In pseudo-static methods, the cyclic earthquake motion is replaced with a constant horizontal acceleration equal to kc (g), where kc is the seismic coefficient, and g is the acceleration of gravity. A force is applied to the soil mass equal to the product of the acceleration and the weight of the soil mass. This method is easy to understand and is applicable for both total and effective stress slope stability analyses. The method ignores cyclic nature of earthquake. It assumes that additional static force is applied on the slope due to earthquake. In actual analysis, a lateral force acting through centroid of sliding mass, is applied which acts out of slope direction. This pseudostatic lateral force Fh is calculated as follows: Where, Fh = horizontal pseudostatic force acting through centroid of sliding mass out of slope direction. m=total mass of slide material W=total weight of slide mass a= acceleration, maximum horizontal acceleration at ground surface due to earthquake amax = peak ground acceleration amax/g=seismic coefficient Inertia Slope Stability – Newmark Method Newmark’s method assumes: existence of a well-defined slip surface, a rigid, perfectly plastic slide material, negligible loss of shear strength during shaking, and that permanent strains occur if the dynamic stress exceeds the shear resistance. Also, the slope is only presumed to deform in the downslope direction, thus implying infinite dynamic shear resistance in the upslope direction. The procedure requires that the value of a yield acceleration or critical seismic coefficient, ky, be determined for the potential failure surface using conventional limit equilibrium methods. Pseudo-static approach Magnitude of slope displacement depends on variety of factors. Higher the ay value, more stable the slope is for a given earthquake. Greater the difference between peak ground acceleration amax due to earthquake and ay, larger the down slope movement. Longer the earthquake acceleration exceeds ay, larger the down slope deformation. Larger the number of acceleration pulses exceeding ay, greater the cumulative down slope movement during earthquake. Most common method used in Newmark method is as follows: Where, d= estimated downslope movement due to earthquake in cm. yield acceleration and peak ground acceleration of design earthquake. Essentially must be greater than . While using Eq. (9.3), pseudostatic factor of safety is determined first using the technique described in Fig. 9.2. If it is less than 1, pseudostatic factor becomes equal to 1. This value of and are used to determine slope deformation. is used to determine is reduced till using Eq. (9.1).