n \u003d 1157.2 / 228.67 \u003d 5.1
we take n \u003d 6.
Fig. 8 Layout of pile clusters
Checking pile bushes for eccentric loading is carried out according to the formulas:
Nmax \u003d (NI + Gr.gr / n) + (Mx ymax / y2i) + (My xmax / x2i);
Nmin \u003d (NI + Gr.gr / n) - (Mx ymax / y2i) - (My xmax / x2i);
where Gr.gr is the average weight of the grillage and soil;
ymax, xmax - distance from the main axis of the grillage to the axis of the calculated piles, m;
yi, xi - distance from the main axis to the axis of each pile, m;
Mx, My - design moments about axes х, у, kNm;
n is the number of piles in the bush;
Gr.gr \u003d bP · LP · dP · CP;
where bP, LP, dP - respectively width, length, depth of the grillage, m;
Rostwerk 4:
Gr.gr \u003d 1.5 * 1.8 * 2.4 * 19.33 \u003d 104.34 (kN)
Nmax \u003d (1157.2 + 104.34) / 6 + 869.67 * 0.9 / 3.6 ^ 2 \u003d 225.7 (kN) 228.67 (kN)
Nmin \u003d (4413.3 + 205.35) / 8-1033.51 * 1.45 / 7.62 \u003d 165.4 (kN)\u003e 0
4.2.6. Calculation of the settlement of the pile foundation.
The settlement of the i-th pile in a group of n-piles with a known distribution of loads between the piles is calculated using the formula from:
where s (N) is the settlement of a single pile, MN, determined by the formula
δij - coefficients calculated by the formula depending on the distance between the i-th and j-th piles; 
Nj is the load on the j-th pile.
Calculation of the settlement of single piles cutting through a soil layer with a shear modulus, G 1 MPa, Poisson's ratio ν 1 and resting on the ground, considered as a linearly deformable half-space, characterized by a shear modulus G 2 and Poisson's ratio ν 2, is allowed to be performed if the requirements and provided 
1 (where l is the pile length, m, d- outside diameter cross-section of the pile shaft, m).
According to clause 7.4.3, the characteristics G 1, and ν 1 are taken as averaged for all soil layers within the immersion depth of the pile, a G 2, and ν 2 - in
within 0.5l. Soil shear modulus 
it is allowed to take equal to 0.4E 0, and the coefficient k ν equal to 2.0 (where E 0 is the total deformation modulus). Estimated diameter d for non-circular piles, calculated by the formula
where A is the cross-sectional area of \u200b\u200bthe pile, m 2.
β- coefficient determined by the formula 7.33
Coefficient corresponding to absolutely rigid pile ();
- the same coefficient for the case of a homogeneous base with characteristics G i and ν i; - relative stiffness of the pile; EA is the compression stiffness of the pile shaft, MN; λ 1 is a parameter characterizing the increase in settlement due to shaft compression and is determined by the formula
;
k ν, k ν 1 are the coefficients determined by the formula
respectively at 
and at;
We calculate the pile foundation No. 1, with the characteristics:
==
Eо1 \u003d 21 * 1.17 + 6.4 * 2 + 6.4 * 1.99 / 1.17 + 2 + 1.99 \u003d 9.71 MPa
G1 \u003d 0.4 * \u003d 0.4 * 9.71 \u003d 3.884MPa;
G2 \u003d 0.4 * \u003d 0.4 * 25 \u003d 1.6 MPa;
poisson's ratio:
For coarse soils =0,27
For sands and sandy loams =0,30
For loams =0,35
For clays =0,42
=
v1 \u003d 0.3 * 1.17 + 0.3 * 2 + 0.3 * 1.99 / 1.17 + 2 + 1.99 \u003d 0.3
2,82-3,78*0,3+2,18*0,3^2=1,88;
β '\u003d 0.17 * ln (2 * 3.884 * 7 / 1.6 * 0.339 \u003d 0.78;
α \u003d 0.17 * ln (2 * 7 / 0.339) \u003d 0.63;
We accept concrete of class B20 with an initial modulus of elasticity in tension Еb \u003d 27 * 10 ^ 3MPa.
EA \u003d 27 * 10 ^ 3 * 0.09 \u003d 2430
χ \u003d 2430 / 3.884 * 7 ^ 2 \u003d 12.768;
λ1 \u003d (2.12 * 12.76 ^ 3/4) / 1 + 2.12 * 12.76 ^ 3/4 \u003d 14.31 / 15.31 \u003d 0.93;
β \u003d (0.78 / 0.93) + (1-0.78 / 0.63) / 3.884 \u003d 0.928;
We calculate the draft of a single pile:
s \u003d (0.928 * 0.228) / 3.884 * 7 \u003d 0.00778m;
We calculate the additional settlement of the pile, located at a distance of a \u003d 0.9 m from the pile, to which the load N is applied Therefore:
4.5\u003e 1, therefore:
a \u003d 0.9 m Δ1.2 \u003d 0.17 * ln () \u003d 0.17 * ln (2 * 3.884 * 7) / 2 * 1.6 * 0.9) \u003d 0.49;
The process of designing a house includes conducting engineering surveys of soils lying on the site allocated for construction, and calculations structural elements buildings. Determination of the shape, structure and dimensions of ground and underground parts buildings are associated with the direction, size and types of loads to be taken. In addition, the specificity of the soil and the detailed features of the house specified in the design assignment are taken into account. All these factors lead to different options and algorithms for calculations. In particular, the construction of an object on weak soils entails calculating the settlement of the pile foundation, which is one of the ways to determine the limiting states of the subgrade.
Regulations
Currently, the latest, updated version of SNiP 2.02.03-85, which covers the design of pile foundations, is SP 24.13330.2011. Certain replacements and amendments have been made to the building rules, but in general, the SNiP norms have not undergone special improvements. However, in case of significant disagreement, preference should be given to the joint venture, rather than relying on SNiP.The set of rules under consideration sets forth the requirements for the design of a certain type of foundation - pile. They indicate different types piles, geological and engineering conditions, are taken into account newly built and under reconstruction structures. But these joint ventures, as well as SNiP, have nothing to do with the pile supports erected:
- under objects with dynamic loads;
- in permafrost conditions;
- for oilfield facilities;
- to a depth of more than 35 meters.
General requirements and types of piles
When designing pile foundations, they are based on:
- engineering and geological surveys;
- features of the structure - structural, operational, technological;
- seismicity of the region;
- the size and direction of payload, as well as temporary loads;
- feasibility studies and comparisons with other options.
In the joint venture and SNiP, the type of piles is determined:
- by the option of deepening - driven and screw, pressed and vibrated, rammed and boring;
- by the method of resting on the ground - standing and hanging;
- by material - wood, metal, concrete and reinforced concrete;
- by the shape of the cross-section and longitudinal section;
- by the presence of reinforcement;
- heel type, etc.
The SNiP states that the calculations of pile foundations should be carried out according to the limit states, divided into two groups. The first relates to the strength of the material, as well as the bearing capacity and stability of the bases. The second relates to the settlement of piles as a result of the action of vertical loads, to various horizontal displacements of underground supports together with soil layers, and, in addition, to the formation of deep cracks in reinforced concrete foundation structures.
The permissible foundation settlement, according to the requirements of SNiP, is calculated according to the second group of limiting states.
An essential point in any calculations is the need to add positive safety factors to the calculation result. The determination of the final indicators is carried out according to variant calculations, after comparing alternative solutions. In certain joint ventures, the calculated values \u200b\u200band the coefficients necessary for the calculations are given, and the acting loads on the foundation, as well as their combinations, are specified. Which building rules establish certain characteristic indicators is indicated in the SNiP.
Calculation of pile settlement
The joint venture provides for several design schemes that take into account the placement of piles relative to each other. At the same time, they are all based on a linearly deformable soil model, but with proper justification, other options can be applied. The main condition for calculating settlements of any type of pile foundations is to determine the value of its possible deformations that do not exceed the limit values.
where S- total draft;
Su - ultimate deformation.
If the conditions are not met, recalculation is carried out with an increase in the depth of the pile supports until the required result is achieved.
According to SNiP, hanging piles are calculated for settlements as a conditional foundation, the boundaries of which at the level of the heel go beyond the total area of \u200b\u200bactually located belts or clusters of piles. The updated version of the joint venture provides for a slightly different calculation algorithm.
Single piles
There are a number of formulas for determining draft:
- hanging piles without widening in the heel zone
where N - received by the pile vertically directed load, MN;
G 1 - shear modulus;
l - the linear size of the pile, namely, its length, m;
β - coefficient
here, d - pile outer diameter, m
If the cross-section is not round, but square, rectangular, T-shaped or I-shaped, then the formula is used to determine the nominal diameter:
here AND - corresponds to the tabulated value of the cross-sectional area.
υ - Poisson's ratio;
parameter that takes into account the increase in the design settlement arising from the compression of the wellbore -
.
- standing piles and hanging piles with widening in the heel area
The values \u200b\u200bof the shear modulus and Poisson's ratio depend on the characteristics of the soil layers. They are taken by layer-by-layer summation and averaging as a result of dividing the resulting figure by the number of layers present within the pile immersion depth.
Dolphin
Calculation of the pile group for settlements is based on the interaction of underground supports with each other. In this case, an additional deformation of the pile located at a certain distance ( ɑ ) from the loaded pile.
If the distribution of loads between piles in one cluster is known, then the following formula is used to calculate the settlement of each of them:
where s (N) - the settlement determined by the above formula (for a single pile);
i and j – i-th and j-th pile;
If the distribution is unknown, then the calculation is made according to the same formula, but taking into account additional nuances and using knowledge of structural mechanics.
Pile field
The figure below shows what the boundaries of the conditional foundation are in relation to the extreme rows of piles:
a) vertically located;
b) obliquely located.
The settlement of the pile field is calculated using the layer-by-layer stacking method. In this case, in the zone of the conditional foundation, the mass of the soil is not taken into account, and only the direct effect of the design forces on the pile foundation is taken into account as a load.
When calculating the layer-by-layer summation method for a pile field, it is taken into account that the total settlement value depends on the pitch of the pile supports within the field area. But here a certain difficulty arises, since the step can have a variable value. In this case, the variant of layer-by-layer summation is complicated by the cell method, using other schemes and formulas in the calculations that are detailed in the SP.
The principle of the layer-by-layer summation method
Its essence is described in SP 22.13330.2011, which are the updated edition of SNiP 2.02.01-83 *. It is as follows. Vertical forces on the foundation are divided into several sections corresponding to the thickness of the soil layers, which are characterized by a homogeneous composition and properties. On settlement scheme the curvilinear diagram changes to a stepped one. In each layer, the compressive work without lateral expansion is determined. In this case, the total draft is calculated by the method of layer-by-layer summation.
In the process of calculation, a stress distribution diagram is built, and in the calculations they use special formulas specified in the joint venture and tables located there. An example of a circuit is shown in the figure below.
Combined foundation
The pile-slab structure of the underground part of the house is used in order to reduce settlement and more even distribution of loads. Such a foundation works effectively in difficult soil conditions, combining load resistance of both piles and slabs. Calculation of the settlement, in this case, includes the definition:
- efforts in piles and slabs;
- deformations and displacements of the combined foundation as a whole, as well as its individual components;
- loads as a percentage on each of the piles and certain sections of the slab.
After performing calculations, taking into account the safety margin, the length and pitch of the pile supports are determined.
Correct calculations and selection of structural elements of the combined foundation will ensure the absence of significant settlements, distortions and rolls of the structure during its operation. Additional calculation conditions are given in SP 24.13330.2011.
When developing a house project, one of the most important stages of work is carrying out geological surveys, which make it possible to determine the composition of the underlying soil, on the basis of which calculations of all structural elements of the structure are carried out. Determination of the size, structure, shape of both underground and surface parts of a building is closely related to the ability of soils to perceive certain types of loads. When erecting a foundation on weak soils, settlement of the pile foundation may occur, in order to avoid which it is necessary to perform calculations that determine the limiting states of soils.
The main document describing the structure and types of foundations on pile supports, as well as regulating their design and calculation is SNiP 2.02.03-85 "Pile foundations".
A more modern document, developed not so long ago, is SP 24.13330.2011. In the modern edition of SNiP, no significant changes have been added, although some replacements and clarifications were made after the appearance of new technologies and materials. In case of doubts and significant disagreements, one should, nevertheless, be guided by the joint venture, which provides specific examples.
The Rules contain the main requests for the development of a specific type of foundation - pile.
The joint venture describes different types supports, engineering and geological characteristics, nuances and particular examples of calculations of newly erected buildings, reconstructed buildings are considered. The provisions of SP 24.13330.2011, as well as SNiP 2.02.03-85, do not apply to pile foundations under construction:
- for structures under dynamic loading;
- in permafrost;
- at a depth exceeding 35 m;
- for facilities related to oil refining enterprises.
Basic provisions
Development of projects and calculation of foundations on pile supports are based on:
- geotechnical survey data;
- seismic categorization of the design area;
- structural, technological, operational characteristics of the structure;
- the meaning and direction of the application of permanent and short-term loads;
- FER when compared with competing options.
Types of pile supports
According to SNiP 2.02.03-85 and more modern SP 24.13330.2011, piles are divided into the following types:
- By the method of deepening - screw, driven, vibro-immersed and pressed, drilling and rammed;
- By the type of ground pressure - hanging and standing;
- By the shape of the cross and longitudinal sections;
- Heel type;
- By materials of manufacture - metal, wood, reinforced concrete and concrete;
- By the presence and method of reinforcement.
Calculation types
SP 24.13330.2011 indicates that the calculation of the foundations is carried out according to critical states, divided into two groups.
For the limiting states of the first group, both stability and load bearing capacity, the strength characteristics of materials are taken into account. The second group concerns the settlement of piles under the influence of vertically applied loads, various displacements of the base in the horizontal plane together with soil layers, the formation of cracks of considerable depth in the body of the structure of reinforced concrete bases.
The permissible settlement of the underground base of the building, according to SNiP 2.02.03-85, must be calculated according to the second group of states.
The most important nuance of calculations is the mandatory acceptance of a safety margin. The final value is taken by calculation for various alternative options and comparison of the data obtained.
In SP 24.13330.2011 the required design values \u200b\u200band constants are presented, the loads on the foundation and their possible combinations are specified.
Performing calculations
Performing a full calculation of the pile foundation is a rather lengthy and complicated procedure. This work can be carried out by a design organization for several days using the appropriate software, the same time an ordinary person will only need to study theoretical information and guidelines.
To calculate the foundation of a private house, you can use a somewhat simplified method, which everyone can easily deal with.
Calculation of the number and amount of settlement of piles
Piles must be placed at the most loaded points of the foundation, namely:
- At the corners of the outer perimeter;
- At the intersection points of the inner walls;
- At the intersection of interior and exterior walls.
The easiest way to determine the location of the piles is to draw a foundation plan on paper on a certain scale. should take no more than 3 m, otherwise additional supports should be installed.
Then it is necessary to determine whether the calculated number of piles and the soil under them are capable of withstanding the weight of the building.
In SP 24.13330.2011, several examples of schemes of the mutual arrangement of piles are given, based on the linearly deformable theory of soils, however, with proper justification, other options can be applied.
When determining the settlement of pile foundations of any type, the basis can be called the calculation of the value of the total settlement S, which should not exceed the maximum permissible deformation Su. That is, the inequality must be observed:
If this condition is not met, then it is necessary to recalculate with a large immersion of the piles to the depth at which the required value will be reached.
According to SNiP, the settlement is defined as a conditional foundation, the boundaries of which on the heel line leave the total area of \u200b\u200breal belts or pile clusters. In the current version of SP 24.13330.2011, the permissible draft is determined by a slightly different method.
Single piles
To calculate the pile foundation of the joint venture with different kinds piles use different formulas.
For piles suspended without expansion in the heel zone, the following expression is valid:
where N is the vertically directed load taken by the pile, MN;
G1 - shear modulus;
l - pile length, m;
β - coefficient equal to:
In this formula, the values \u200b\u200bof α and ß are determined from the expressions:
here, d is the diameter of the pile along the outer contour, m.
If the cross-section of the pile is rectangular, square, T-shaped, or I-shaped, then the diameter d is determined from the identity:
In this formula, A is the cross-sectional area taken from the tables of the joint venture, m2.
where υ is Poisson's ratio;
The relative stiffness of the pile is determined from the expression:
In this formula, EA indicates the compression stiffness of the barrel.
The parameter that determines the increase in the calculated settlement due to the compression of the wellbore can be determined from the ratio:
For standing and hanging piles with widening in the heel zone, the total draft is determined by the formula:
Where db means the diameter of the pile expansion at the bottom.
The values \u200b\u200bof Poisson's ratio and shear modulus depend on the properties of the soil layers and are taken by the method of layer-by-layer summation and obtaining the average value by dividing the obtained value by the number of soil layers within the pile depth.
Calculation of the settlement of the pile "bush"
Calculation of the settlement of a group of piles is based on their interaction with each other. In this case, it is necessary to determine the additional deformation of the pile located at a distance a from the pile operating under load.
For this, the following expression applies:
With a known distribution of loads between piles, the value of the settlement of any of them can be calculated from the equality:
where s (N) is the draft calculated from the expression for a single pile.
With an uncertain distribution, the calculation is performed according to the same formula, but it is necessary to take into account some nuances and have certain knowledge in the field of structural mechanics.
Calculation of the pile field
In this case, calculations are performed by a different method, different from the options already considered, according to the formula:
where sef is the subsidence of the conventional base;
∆sp is the amount of additional settlement that occurs when the piles are pushed at the level of the base of the conventional foundation;
∆sc is the value of additional settlement arising from compression of the pile shaft.
The settlement of the pile field is also determined by the layer-by-layer stacking method. In this case, in the area of \u200b\u200bthe conditional foundation, the weight of the soil can be neglected, and only the direct influence of the design forces on the pile foundation is taken as the load.
To perform calculations by the method of layer-by-layer summation, it is necessary to assume that the total value of the settlement value depends on the interval between the pile supports in the clear within the boundaries of the area of \u200b\u200bthe pile field.
In this case, you can face significant difficulties, because the distance between the piles can be different. Then the method of layer-by-layer summation has to be complicated to the cell method, using other formulas and schemes that are also available in SP 24.13330.2011 when performing calculations.
General principles of layer-by-layer stacking
The method is detailed in the Building Regulations 2011. In short, it can be summarized as follows.
Vertical loads on the base are divided into smaller sections, coinciding in thickness with soil layers, characterized by the same composition and identical properties throughout the volume. In the calculation scheme, the curved plot is replaced by a stepped one. The compressive work of each layer is determined without taking into account the lateral expansion of the soil. The total settlement value is calculated using the layer-by-layer method.
In parallel with the calculations, a stress distribution diagram is drawn, and for the calculations, the special expressions specified in the joint venture and the tabular values \u200b\u200bof some indicators are used. Also in the joint venture there is an example of a calculation scheme.
Calculation of the combined foundation
The pile-slab structure of the underground part of the structure is often used to reduce settlements and to uniformly apply existing loads. Foundations of this type are quite effective to use for complex soils, involving a simultaneous combination of resistance to loads and slabs and piles.
To perform the calculation, it is necessary to determine:
- Loading in slab and piles;
- The percentage of loads transferred to each of the piles and each of the slab zones;
- Deformation and shears of the combined base and its individual elements.
Upon completion of the calculations, the step and length of the pile supports are calculated with the obligatory application of the reliability factor, the value of which is taken according to SP 24.13330.2011, depending on the number of piles accepted.
The accuracy of calculations and correct selection structural elements of the combined base can guarantee the absence of significant settlement, as well as rolls, distortions, the appearance of cracks on the surface of the walls of the structure.
How not to be mistaken in the absence of experience
With soil group
Pile foundation is a good choice for clay soils The basis in calculating and determining the feasibility of erecting a pile, as, indeed, any other foundation, is the identification of the type of soil.
Soils can be conditionally divided into several groups:
- Rocky (rocky) soil itself can represent solid foundation for building a house, because there is no point in building a pile foundation on it;
- On sandy soils (as well as on "gristly" - a mixture of sand, gravel, clay) there is also no special need to install piles - it is best to arrange shallow piles on them. strip foundations, naturally, below the depth of freezing;
For clayey soils with diametrically opposite characteristics (heaving, plasticity), pile foundations are an ideal and, often, the only correct solution.
- On loams and sandy loams, evenly folded, it is quite possible to build a house on a strip foundation;
- Peat bogs only allow light slab structures to be erected. Watch the video on how not to be mistaken with the type of foundation.
With the number of piles
To use the fairly complex calculations described above, simple rules selection of the number of piles in accordance with the distribution of control points along the perimeter of the structure:
- Under the frame-panel and wooden houses the interval between piles should not exceed 3 m;
- For lightweight concrete structures, the distance between buried supports should be taken no more than 2m.
The simplest and most understandable is the following example.
A house plan is drawn on a sheet of paper to scale. At the corners and intersections of the walls, points are outlined at which piles should be installed first of all. Further, the rules for placing supports described just above are applied depending on the material from which the building is being erected. Watch the video on how to calculate the number of piles.
Under the stoves and massive fireplaces, it is necessary to provide for the installation of two piles, and also take into account the presence of a veranda and other annexes.
No matter what materials the house is built from, no matter what size and design features it has - the calculation of the pile foundation as supporting structure the whole structure can be called the main nuance of a successful construction.
