4.2.3. Calculation of settlement of foundations by the method
layer-by-layer summation
This method is recommended by SNiP 2.02.01 - 83 * when calculating the settlement of foundation foundations. The method is based on the following assumptions: the foundation settlement is determined along the vertical central axis of the foundation base; when determining stresses, the soil is considered as a linearly deformable body (the heterogeneity of the base is taken into account when determining the deformations of each soil layer); settlement is caused only by the action of additional vertical stresses; foundations are not rigid; deformations are considered only within the compressible strata H squeeze determined by the condition
,
(4.11)
where 
- vertical additional stresses; 
- vertical natural stresses (Fig. 4.6).
,
where 
- area of \u200b\u200bthe foot of the foundation; 
- natural soil pressure at the level of the foundation sole.
Due to a gradual change in stresses along the depth of the base, its thickness can be divided into a number of layers so that the soil is homogeneous within each layer; while the thickness of each layer should be no more than 0.4 b and tension calculated from the load at the boundary of the layers by the formula
,
(4.12)
in 
which 
determined by table. 3.2 and plot these stresses. Then plot the stress of natural soil pressure along the axis of the foundation
,
(4.13)
here 
and 
– specific gravity soil and the thickness of each layer.
Lower limit of compressible strata BC defined graphically by overlaying the plot diagrams reduced by a factor of five.
The total foundation settlement is determined by summing the settlement of individual layers within the compressible strata:
,
(4.14)
where 
=
0,8;n - the number of layers within the compressible strata; - thickness i-th soil layer; 
- deformation modulus ith layer of soil.
4.2.4. Subgrade settlement over time
If water-saturated clayey soils lie at the base of the foundation, sediment can develop for a long time. A long process of sediment development is associated with a very low rate of water filtration in clayey soils (filtration coefficient of the order of 10 -7 ... 10 -10 cm / s) and slow compaction of water-saturated soils.
Recall that soils with a water saturation coefficient are water-saturated 
>
0,8.
Modern methods of forecasting the development of soil deformations in time are based on the theory of filtration consolidation.
The one-dimensional problem of the theory of filtration soil consolidation, first formulated by prof. Tertsagi (1924), was further developed in the works of professors N.M. Gersevanov, V.A.Florin, N.A. Tsytovich, Yu.K. Zaretsky, etc.
The Tertsagi-Gersevanov theory, developed for the one-dimensional problem of consolidation of a homogeneous soil layer, is based on the following prerequisites and assumptions:
1) the soil is homogeneous and completely saturated with water;
2) the load is applied instantly and at the first moment of time is completely transferred to the water;
3) the rate of subsidence of the soil base is determined by the rate of squeezing water out of the pores;
4) the movement of water in the pores of the soil occurs in the vertical direction and obeys Darcy's law of laminar filtration (2.17).
Let us consider the solution of the one-dimensional problem of the theory of filtration consolidation according to Tertsagi-Gersevanov, which is currently the theoretical basis for calculating the sediment of bases in time. According to these premises, the process of sedimentation in time under the influence of a constant continuous uniformly distributed load in conditions of one-sided water filtration is determined by the laws of filtration and compaction (2.9).
At the initial moment of time t 0
, immediately after application of the load, external pressure r completely transferred to pore water 
, i.e. 
, and the pressure on the mineral part of the soil 
... However, at the following times t 1 ,t 2 ,…,
t n the pressure in the water will decrease, and the pressure on the mineral particles of the soil will increase, and at any time
(4.15)
and at the end of consolidation, all external load will be absorbed by the mineral particles of the soil ( 
) (fig. 4.7).
Soil layer thickness h underlain by an incompressible waterproof base. Intensity load r acts on the soil through the drainage layer. Therefore, as the soil settles, water will be squeezed out of it in one direction (upward). As water is squeezed out of the pores, the soil will be compacted (porosity decreases). Water consumption dqextruded from the elementary layer dz at a depth z (Figure 4.7), will be equal to the decrease in soil porosity dn for a period of time dt, i.e.
.
(4.16)
The minus sign indicates that with an increase in water consumption, the soil is compacted and its porosity decreases. After a series of transformations using the laws of laminar filtration and compression, equation (4.16) can be represented for a one-dimensional problem in the form of a partial differential equation
,
(4.17)
where 
- the consolidation coefficient, the value of which depends on the properties of the soil,
,
(4.18)
here 
- filtration coefficient; 
- coefficient of soil compressibility; e- coefficient of porosity; 
- specific gravity of water.
The solution to equation (4.17) is found by applying Fourier series (i.e. trigonometric series) with the following boundary conditions:
1) t
= 0;
=
0;
2) t = ∞;
=r;
where m - positive integer number of natural series, m = 1,3,5,…, ∞;
–Indicator of consolidation, (4.20)
h - layer thickness; t - time from the moment of loading.
If voltage is known in layer dz during t from the moment of loading, then the sediment of this layer follows from the expression (4.10):
.
Slump layer thickness h during t find by integrating the resulting expression from 0 to h:
In this expression, the part before the integral is the final draft, and the part 
can be defined as sediment consolidation rate
Uequal to the ratio of unstabilized sediment 
to the final 
, i.e.
.
(4.21)
After integrating (4.21), we obtain
.
The quantities U and N functionally related. Table 4.1 given the values N for different variants of sealing stress diagrams (Fig. 4.8).
Option 0 corresponds to the compaction of the soil layer under the action of a continuous load. The diagram of sealing pressures is rectangular. Option 1 occurs when the soil is compacted under the pressure of its own weight, option 2 - when the compaction stress decreases with depth according to the law of the triangle.
By setting different values \u200b\u200bof the degree of consolidation U, according to table. 4.1 define N and find time for a given degree of consolidation:
.
(4.22)
Under the influence of the load from the structure, its base is deformed and gives a draft, and in some cases, a subsidence.
Settlement of the base (or settlement of the foundation) is the vertical movement of the soil surface under the base of the foundation, associated with the transfer of the load from the structure to the base.
Distinguish between uniform and uneven base draft. With a uniform settlement, the displacements of the points of the soil surface under the entire area of \u200b\u200bthe foundation are the same, and with an uneven settlement, they are not the same. Uniform settlement of the base is generally not hazardous; uneven settlement often becomes the cause of the violation of the conditions of normal operation of structures, and sometimes their accidents.
To compact the soil under load, a certain time is required, during which an increase in the subsidence of the base is observed. The settlement corresponding to the final compaction of the soil is called complete, final or stabilized.
A large, rapidly flowing sediment, accompanied by a radical change in the composition of the soil, is called subsidence. Subsidence is observed, for example, when the soil bulges out from under the base of the foundation and when macroporous soils are soaked under load.
§ 22. Methods for calculating settlement
The compaction settlement is calculated on the assumption that the soil obeys the laws of a linearly deformable medium, when the deformations linearly depend on pressures. Theoretically, the maximum ground pressure at which there is a linear relationship is determined by the absence of plastic zones under the base of the foundation. However, observations of structures show that a slight development of zones of plastic deformation under the edges of the foundation can be tolerated.
To determine the final settlement of the base, the layer-by-layer summation method is widely used. In this case, it is believed that the foundation settlement occurs as a result of compaction of a certain soil layer of limited thickness, called the active zone. The lower boundary of the core is taken at the depth da from the base of the foundation, at which the additional pressure (under the center of gravity of the base) from the load transmitted by the foundation is 20% of the household (natural) pressure.
With a foundation located on the ground surface, additional pressures рz, kPa, are determined by formula (2.7), and with a foundation buried in the ground, by the formula
Pz \u003d a (p0-pg), (4.1)
where a is the coefficient taken according to table. 2.1; p0 - normal stresses along the base of the foundation, kPa; pg is the household pressure at the depth of the foundation base, kPa.
The arrangement of supports in the river bed causes constriction of the channel and can lead to intense soil erosion, especially at the supports. As a result, the household soil pressure decreases. Household pressure is substituted into formula (4.1), calculated without taking into account soil erosion, i.e., the pressure with which the soil was compressed before the construction of the structure. This is due to the fact that, after unloading the soil, its deformations during repeated loading are initially very small; they begin to increase noticeably only when the stresses in the soil reach the values \u200b\u200bthat were available before unloading.
The active zone of the soil is divided into horizontal layers with a thickness of no more than 0.4b, where b is the smallest size of the foundation in the plan, m. If within the core there is a stratification of different soils, then their boundaries are taken as the boundaries of the selected layers. Settlement s of the base is determined by summing the deformations of individual layers. The deformation si m, of each i-th layer is calculated on the assumption that soil compaction occurs in the absence of lateral expansion (in conditions of compression compression) at a constant pressure pz kPa; the latter is taken to be equal to the average additional pressure pg, kPa, from the pressures arising at points under the center of gravity of the foundation base within the layer under consideration.
Using the formula (1.29) to determine the deformation of the soil under compression, we can write:
si \u003d eiti \u003d (piβi / Ei) li (4.2)
where ei is the relative deformation of the soil of the i-layer; ti - thickness of the i-th soil layer, m; βi is the coefficient taken according to table. 1.3
depending on the type of soil of the i-th layer; Ei - modulus of deformation of the soil of the i-th layer, kPa, determined by the formula (1.28) based on the results of testing soil samples for compression.
The processes of subsidence of the base of the building, which are characterized by an uneven manifestation, are the most common and often manifested defect of foundations. different types... It is the uneven settlement of the foundation that leads to cracking of the base of the building and its walls, and this can cause the most unpleasant consequences. Skewing of a building is the most common negative manifestation of this subsidence of the foundation.
Settlement is the vertical displacement of the foundation that occurs as a result of deformation of the soil layer under the sole. On this moment There are many reasons for the occurrence of sedimentary processes at the base of a building. The most common reason is excessive savings in material resources, both in construction operations and in organization. earthworks (for example, hiring unskilled workers). Due to insufficient funding construction works you can incorrectly calculate the depth of laying the foundation in the ground. If you laid the base significantly higher than the norm, then such an error will be almost impossible to correct with the help of subsequent renovation works... Also, too much groundwaterthat take place in the area of \u200b\u200bbuilding construction and laying the foundation. In this case, this problem can be beaten with the help of a competent effective device, the installation of which is usually carried out on initial stage building a house. If you equip the site with drainage with an already erected building, this will attract some difficulties, the solution of which will require additional costs. Even in this case, trees can be planted in the area around the building, which will quickly absorb excess liquid due to their developed root system.
Defects in the base can also occur due to the long service life of the structure. But most often the settlement of a deformed foundation is manifested as a result of the appearance of defects in its design, which arise due to poor-quality selection building materials... This deficiency can only be corrected with the help of a major overhaul, but this does not always help. It is guaranteed that the foundation can be fixed only after the complete replacement of the entire foundation. However, this can be done using special equipment, which is quite expensive.
Deformation processes of the foundation can also occur in the process of adding extra floors over the entire area of \u200b\u200bthe building or on any part of it. This problem can be corrected by saturating the soil directly under the base, as well as at a short distance from it, with "cement milk".
To prevent subsidence of the building base, the following steps should be taken. First of all, you need to provide the foundation with competent protection against moisture. For this, the base must be insulated from contact with the liquid with special materials that have waterproof properties. Bitumen and roofing felt are considered the cheapest, most affordable and practical. It is also possible to insulate the substrate from moisture using high quality waterproofing materials such as liquid glass in combination with cement. It is also recommended to equip a special ventilation system, thanks to which excess moisture will evaporate on its own. To do this, you can only equip additional ones, which are manufactured in accordance with the proper technology of the base ventilation device.
Also, to prevent the foundation from settling, it is necessary to install blind areas in an inclined area, coming from the base, from concrete or asphalt, as well as arrange a reliable and effective system for draining moisture from the roof surface. It should be noted that the subsidence coefficient of the base is directly proportional to the value, which is the depth of soil freezing in a given area. So it is necessary to carefully develop a construction project, as well as to choose the right materials for construction work, then the result will be a reliable and durable building, and the likelihood that a settlement of the laid building will occur will be minimized.
Calculation of the foundation settlement
There are several ways to calculate the foundation draft. The main and most proven method for determining the final, total settlement is the method of summing the settlement of individual layers. For each of the layers, it is necessary to determine its value for the degree of deformation. The layers should be considered within a certain soil thickness - in the core, and deformations that occur below this soil level can be excluded. The method of summing the sediment of individual layers can be used to determine any sediment.
The settlement can also be calculated using the equivalent layer method, which allows to determine the settlement taking into account the limited lateral expansion. An equivalent layer is a soil thickness that, under conditions of the impossibility of lateral expansion (when the entire surface is loaded with a continuous load), gives a draft, which is equal in size to the settlement of a foundation that has limited dimensions under a load of the same intensity. That is, in this case, the spatial problem of calculating the settlement can be replaced by a one-dimensional one.
Maximum permissible settlement of foundations
To date, there is no convincingly substantiated standard value of the maximum permissible additional settlement of buildings. Normally, regulations do not distinguish between the initial, obtained during construction, and the additional draft. The maximum average draft of a brick building according to the documents is approximately 10-12 cm.
It is worth noting that the initial settlement of the foundation on a homogeneous soil base is uniform over the building spot, therefore, even with a large permissible average settlement (10-12 cm), the requirements for uneven settlement are also satisfied. And, as you know, the result of unevenness are distortions of the building and the occurrence of cracks.
According to the standards, the maximum permissible draft for buildings of the 1st category of technical condition is 5 cm, and for buildings of the 2nd and 3rd categories, which already have deformations - 3 and 2 cm.
As observations show, brick buildings of the 1st and 2nd category of condition with a local additional draft of 5 cm can receive serious damage. Through cracks will form in the walls, and when a vertical crack occurs, its opening is comparable to the amount of settlement. The displacement of prefabricated floor slabs along the support areas is very close to the limit. In this case, the renovation of the building will require the eviction of the tenants, selective reinforcement of the structure and restoration of the interior and exterior decor. With precipitation of 3 and 2 cm, smaller repairs will be required. So can a foundation draft of 2-5 cm be considered permissible? Of course, if the absence of collapse of structures is taken as the criterion of admissibility, and it is impossible, if the criterion of admissibility is the absence of damage that requires repair.
