# Artux Foundation

Seismic Bearing Foundation,

similar to a non seismic slab-on-grade

The effect of horizontal earthquake body forces on the bearing capacity of foundations has been examined computationally in a rigorous manner by employing the method of stress characteristics. The bearing capacity factors Nc, Nq and Nγ, due to the components of soil cohesion, ground surcharge pressure and soil unit weight respectively, have been plotted as a function of earthquake acceleration coefficient (αh) for different values of soil friction angle (Φ). The inclusion of earthquake body forces causes a considerable reduction in the bearing capacity factors. The bearing capacity factors Nc and Nq are seen to be approximately of the same magnitude as those reported in the literature on the basis of different solution methods. However, the obtained values of Nγ are found to be significantly smaller than the available results. The nature of the pressure distribution along the footing base and the geometry of the observed failure patterns vary with the consideration of earthquake body forces.

I once tried to develop a correlation proposed by Paolucci & pecker (1997), which turned out to be totally and unrealistically conservative.

So you have to factor in structural inertia and, sometimes but not often, soil inertia.

The seismic wave hits the foundation. The structure sways according to its vibrational modes. The main mode can be computed by a simple correlation, sometimes it is enough to take, very simply, T = 0.1*# floors (period in seconds).

Then you should use such period to find the base shear, or soil reaction against the structure, I use the dissipative spectra calculated according to regulations, as an input you need the structural factor of dissipation.

The structure sways, dissipates the seismic energy in microfractures at plastic hinges, then imposes back such signal to the soil. This is structural inertia, which tends to dampen the soil seismic signal.

If W = weight force,  Kh*W = H, the horizontal component of seismic force, and you can use H as an input for the inclined loads formulas in Hansen, Meyerhof, vesic (details in Bowles).

Foundation eccentricity must be given by the structural engineer. Then you have (at last) all which is needed to figure out seismic bearing capacity.

Richards et al.  proposed a slightly different method, featured by Das (shallow gfoundation handbook) and such method is similar to the article suggested by BigH.

Soil inertia should be calculated only with very large foundations, tall & slender structures, very soft soils.

I use the correction factors given by Poolucci & Pecker (1997).

Since EC8 gives no other indications,as far as I see, in the first stage the engineer should decide which main group the soil belongs to: frictional behaviour or cohesive behaviour. This controls which of the two 14-elements coefficients vector shall be used. They are discrete and not continuos values, again, they say nothing about intermediate values (unless otherwise specificed in the original paper but since everyone is ignoring this aspect I'll reasonably assume there are no intermediate values)

A very simple algorithm in pseudo-code could look like the following:

If (soil = frictional and soil = dense

then     vector = B; gamma_RD = 1;

If (soil = frictional and soil = loose_dry)

then     vector = B; gamma_RD = 1.5;

If (soil = frictional and soil = loose_wet)

then     vector = B; gamma_RD = 1.50;

If (soil = cohesive and soil = sensitive)

then     vector = A; gamma_RD = 1.15;

If (soil = frictional and soil = not_sensitive)

then     vector = A; gamma_RD = 1;

else output: 'error - please check the input data!'

where vector A is of course the set of 14 coefficients to be used in the case of cohesive, non-frictional material, and vector B conversely the related set for frictional soil.

Field and laboratory observations of seismic settlements of shallow foundations on granular soils that are not attributable to changes in density or liquefaction are explained in terms of seismic degradation of bearing capacity. Limit analysis using a Coulomb-type mechanism including inertial forces in the soil and on the footing gives expressions for seismic bearing capacity factors that are directly related to their static counterparts. Comparison of the two depicts clearly the rapid deterioration of the overall foundation capacity with increasing acceleration. Such periodic inertial fluidization causes finite settlements that are possible even in moderate earthquakes. Reduction in foundation capacity is due to both the seismic degradation of soil strength and the lateral inertial forces transmitted by shear to the foundation through the structure and any surcharge. A straightforward sliding-block procedure with examples is also presented for computing these settlements due to loss of bearing capacity for short time periods. This approach also leads to a design procedure for footings based on limiting seismic settlements to a prescribed value.