SOIL

The value of the elastic foundation coefficient C₁ at the design point with coordinates (x, y) is determined by the formula:

The value of the elastic foundation coefficient C₁ at the design point with coordinates (x, y) is determined by the formula:

where q is the value of the uniformly distributed load at the design point with coordinates (x, y).

The value of the elastic foundation coefficient C₁ at the design point with coordinates (x, y) is determined, as in Method 1, by the formula:

with the difference that when determining the average deformation modulus E₀, a correction coefficient K_j is taken into account, and the additional vertical stress is distributed uniformly with depth:

The same coefficient is also introduced when determining the settlement:

It is assumed that the coefficient K varies from 1 to 12 according to a quadratic parabola law within the compressible stratum H_c

For Methods 1 and 3, the value of the elastic foundation coefficient C2 at the design point with coordinates (x, y) is determined by the formula

For Method 1, this formula can be written as

Savinov's formula makes it possible to determine the elastic foundation coefficient C1 under dynamic effects on the foundation, and looks as follows:

C₀ – soil elasticity constant, tf/m³;
U – foundation perimeter, m;
F – foundation area, m²;
p – average pressure under the footing,
p₀ – pressure on the test plate, equal to 2 tf/m²;
Δ – elastic constant of the foundation, taken equal to 1 m^-1.

Formula 4 makes it possible to determine the coefficient of elastic uniform compression Cz (C1z) under dynamic effects on the foundation, and looks as follows:

b₀ – coefficient, m^-1, which is taken equal to 1 for sandy soils, 1.2 for sandy loams and loams, and 1.5 for clays and coarse clastic soils;
E – deformation modulus of the soil under the foundation footing, kPa (tf/m2), determined in accordance with the requirements of SNiP 2.02.01.83;
А₁₀ = 10 m²;
А – area of the foundation footing, m².

This method is based on the Pasternak model, according to which the elastic foundation coefficient C1 is calculated by the formula:

where Н_с is the depth of the compressible zone, μ₀ is the average value of Poisson's ratio, E₀ is the average value of the soil deformation modulus.

When calculating for dynamic oscillations, three types of soil particle motion are considered: translational motion along the z-axis and two types of oscillations (about the x-axis and the y-axis). Therefore, instead of a single value of the elastic foundation coefficient С1, three values are considered (C_z, C1_xx, C1_yy), each of which reflects the behavior of the elastic foundation in the specified direction resulting from the corresponding type of particle motion. This is therefore written as follows:

Where Z_pz is the thickness of soil required for analyzing the foundation behavior under translational motion of soil particles, and Z_pxx, Z_pyy are the thicknesses of soil required for analyzing the foundation behavior under oscillatory motion.

In the calculation for Method 6, Poisson's ratio μ is determined from the ratio between the propagation velocities of transverse and longitudinal dynamic waves and is calculated using the formulas:

Where V_soz, V_soxx, V_soyy are the propagation velocities of transverse waves, and V_poz, V_poxx, V_poyy are the propagation velocities of longitudinal waves.

The wave velocities V_soz, V_soxx, V_soyy, V_poz, V_poxx, V_poyy used to calculate the elastic foundation coefficients are determined as the load-weighted arithmetic means of the averaged wave velocities at each point. The values of the averaged wave velocities at each load point are calculated using the formulas:

Where V_si, V_pi are the experimental values of the propagation velocities of transverse and longitudinal waves in an elementary soil layer, specified by the user.

When calculating the elastic foundation coefficients C1_Z, C1_XX, C1_YY, the values of effective elastic moduli are used, which are calculated using the formulas:

Where G_z, G_xx, G_yy are the values of the effective shear moduli, determined by the formulas:

Where a is a coefficient taken from Table D.2 of document [1]. This coefficient depends on the design acceleration of the foundation (as a fraction of g), which is taken from the initial data.

Where ρ_z, ρ_xx, ρ_yy are the average specific masses of the soil, determined in the same way as the propagation velocities of transverse and longitudinal waves used in calculating Poisson's ratio. That is, the values ρ_z, ρ_xx, ρ_yy are calculated as the load-weighted arithmetic means of the averaged unit weight values ρ_z, ρ_xx, ρ_yy at each point, calculated using the formulas:

Where ρ_i is the unit weight value of the i-th soil layer, taken from the "Soil Characteristics" table.