## R

Fig. 18.9. For the calculation of bearing capacity of posts (a) and piles (b) for foundations in the permafrost.

Stability of the foundation is calculated from bearing capacity using the following formula:

where N is the design load on the base; is bearing capacity of the base; kr is the factor of safety (used in accordance with the class of structure with respect to the Norms).

The design load N on the foundation base includes the weight of the structure above the foundation with its effective load and the weight of the foundation proper (from the level of a cellar ceiling to the base of the foundation).

Bearing capacity of the base includes the shearing strength of the frozen ground along the adfreezing surface of any part of the foundation frozen into the permafrost and the resistance of the permafrost to pressure normal to the foundation base (Fig. 18.9). For post and pile foundations:

where m is the coefficient depending on the type and structure of the foundation, varying in the range from 1.2 to 1.1 according to the Building Norms; Radi is the design shear strength of the i-th layer along the adfreezing surface of the foundation; R is the design resistance of the frozen ground to normal pressure; Fad. is the area of the i-th layer of the side surface; F is the area of the foundation base.

Values of i?ad and R are set equal to the values of long-term shearing and

compressive strengths and depend on ground composition, ice content and temperature at the depth at which the foundation is laid.

The permafrost possesses plastic properties, i.e. the capacity to deform under the effect of long-term loading, especially at temperatures close to 0°C. A stability assessment for deformations is performed, to establish that:

where Sper is the limiting permissible deformation of the base and structure determined in accordance with the type of the structure and the particular features of the foundation and structure; S is the value of the deformation of the ground base depending on the pressure around the base of the foundation and the composition and properties of the frozen ground (strain modulus or compressibility factor).

The conditions (18.1-18.3) are responsible for the stability of the foundation base depending on the strength and strain properties of the permafrost. However during the period of seasonal ground freezing the foundation is subjected to heaving forces directed vertically upward and tending to lift, or to 'pull out' the foundation from the perennially frozen ground. Two types of heaving forces, normal and tangential, are distinguished. Normal forces are exerted normally to a foundation base situated in the layer of seasonal freezing or thawing. They must be considered in the design of shallow foundations (see Fig. 18.1).

Forces of heaving resulting from the adfreezing of the frost-susceptible ground to the side surface of the foundation are exerted at a tangent to its surface. These forces are considered in the design of the basic types of foundations, the depth of which must be greater than the normative depth for seasonal ground thawing or freezing in the area, according to Building Norms and Regulations II-18-76. The normative depth of the seasonal ground thawing is defined as the greatest depth observed over a period of no less than 10 years, at sites free of vegetation and peat cover, and where the snow cover disappears in spring. This depth is taken to be equal to the mean depth of maximum annual seasonal freezing in accordance with observational data for the period of no less than 10 years, for open ground, free of snow, with the groundwater level situated below the depth of the seasonal freezing.

Foundation tolerance for the effect of heaving forces is calculated, on the basis that the heaving forces against the foundation should be smaller than those keeping the foundation from being heaved (Fig. 18.10):

where Pheav is the specific tangential force of heaving; F is the area of side surface of the foundation situated in the layer of seasonal freezing or thawing; N is the design load on the foundation including structure and foundation pressures; P is the design value of the force keeping the foundation from being heaved; m is a coefficient of work conditions equal to 1 according to the Building Norms and Regulations; kr is the safety factor taken to be equal to 1.1.

In the case when a foundation is situated in perennially frozen ground (see Fig. 18.10), the value P is defined by the shearing strength, Rad, of the frozen ground along the adfreezing surface and by the area of vertical adfreezing surface Fad equal to the product of the foundation periphery and the depth of placement in the perennially frozen ground:

If the foundation is situated within the unfrozen seasonally freezing ground, the forces keeping it from being heaved are defined by friction resistance of the unfrozen ground along the friction surface/unf and by the area of the friction surface Ff fri*

The specific tangential forces of heaving depend on composition, moisture content, depth of ground freezing and the material of the foundation in volved in the adfreezing. Their value varies from 0.05 to 0.13 MPa. When the depth of seasonal freezing is greater than that of the placing of the foundation, the normal forces of heaving are engaged and their value is added to the left part of the equation (18.4). This places fundamentally more stringent requirements upon the foundation structure, because the value of the normal forces of heaving is significantly (sometimes an order of magnitude) greater than that of the tangential forces.

It follows from the formulae (18.2) and (18.4) that the bearing capacity of the base and the forces keeping the foundation from being heaved depend on composition, properties of ground and, in addition, are in direct proportion to the area of the foundation side surface situated in the permafrost. It follows herefrom that one will be able to fulfil the conditions (18.2) and (18.4) and justify the selection of optimal sizes for foundations, ensuring structural stability, by changing the foundation area, increasing or decreasing the depth of its placement into the frozen ground and using various constructive solutions.

The depth of seasonal thawing on which the total value of heaving forces depends is also susceptible to control. By achieving its reduction and using types of foundation having minimal area of adfreezing with the seasonally thawed ground layer, one can decrease the values of heaving forces by limiting the placement depth of the foundation.

However, it is not always possible to achieve stability of the structure under design with the help of constructive solutions only and these solutions may turn out to be economically unattractive. In these cases there is a need to use methods aimed at changing the properties of the ground.

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