Influence of earthquake

Earthquake increases the effect of active pressure and reduces the effect of passive pressure. The theories used in our programs (Mononobe-Okabe, Arrango) are derived assuming cohesionless soils without influence of water. Therefore, all inputted soils are assumed cohesionless when employing these theories to address the earthquake effects. Earthquake effects due to surcharge are not considered in the program – the user may introduce these effects (depending on the type of surcharge) as "Applied forces"

The coefficient k_h is assumed always positive and such that its effect is always unfavorable. The coefficient k_v may receive both positive and negative value. If the equivalent acceleration a_v acts downwards (from the ground surface) the inertia forces k_vW_s will be exerted on the soil wedge in the opposite direction (lifting the wedge up). The values of equivalent acceleration a_v (and thus also the coefficient k_v) and inertia forces k_vW_s are assumed as positive. It is clearly evident that the inertia forces act in the direction opposite to acceleration (if the acceleration is assumed upwards – a_v = - k_v*g then the inertia force presses the soil wedge downwards: -k_vW_s. The direction with most unfavorable effects on a structure is assumed when examining the seismic effects.

For sheeting structures it is possible to neglect the effect of vertical equivalent acceleration k_vW_s and input k_v = 0.

Sign convention

The seismic angle of inertia is determined from the coefficients k_h and k_v (i.e. angle between the resultant of inertia forces and the vertical line) using the formula:

where:	kv	-	seismic coefficient of vertical acceleration
	kh	-	seismic coefficient of horizontal acceleration

Pressure from seismic effects

Increment of active earth pressure due to seismic effects (computed from the structure bottom) follows from:

where:	γi	-	unit weight of soil in the ith layer
	Kae,i	-	coefficient of active earth pressure (static and seismic) in the ith layer
	Ka	-	magnitude of earth pressure in the ith layer due to Coulomb
	hi	-	thickness of the ith layer
	kv	-	seismic coefficient of vertical acceleration

Reduction of passive pressure due to seismic loading (computed from the structure bottom) is provided by:

where:	γi	-	unit weight of soil in the ith layer
	Kpe,i	-	coefficient of active earth pressure (static and seismic) in the ith layer
	Kp	-	magnitude of earth pressure in the ith layer due to Coulomb
	hi	-	thickness of the ith layer
	kv	-	seismic coefficient of vertical acceleration

Active earth pressure coefficients K_ae,i and K_pe,i are computed using the Mononobe-Okabe theory or the Arrango theory. If there is ground water in the soil body the program takes that into account.

The basic assumption in the program when computing earthquake is a flat ground surface behind structure with inclination β. If that is not the case the program approximates the shape of terrain by a flat surface as evident from figure:

Terrain shape approximation

Point of application of resultant force

The resultant force is automatically positioned by the program into the center of the stress diagram. Various theories recommend, however, different locations of the resultant force – owing to that it is possible to select the point of application of the resultant force in the range of 0,33 - 0,7H (His the structure height). Recommended (implicit) value is 0,66H.  Having the resultant force the program determines the trapezoidal shape of stress keeping both the inputted point of application of the resultant force and its magnitude.