The main condition that must be met when designing foundations is:
where: P is the average pressure under the base of the foundation of the accepted dimensions
where: - design load on the edge of the foundation in a given section, kN/m;
Foundation weight per 1 running meter, kN/m;
Weight of soil on foundation ledges, kN/m;
b - width of the foundation base, m;
R - calculated soil resistance under the base of the foundation, kPa
where: - weight of the slab per 1p. m., kN/m;
Weight of foundation blocks per 1 running meter, kN/m;
Weight of brickwork per 1 running meter, kN/m;
where: - weight of the soil on 1 ledge (without concrete), kN/m;
Weight of soil on the 2nd ledge (with concrete), kN/m;
where: - width of the soil on the ledge, m;
Height of soil on the ledge, m;
g"II - averaged value of the specific gravity of the soil lying above the base of the foundation;
where gсf =22 kN/m.
Section 1 -1
n"g= n""g=0.6 1 0.62 16.7+0.6 0.08 1 22=7.2684 kN/m
349.52 kPa< 365,163 кПа, проходит по напряжениям - принимаем.
Section 2 -2
n"g=0.75 1 1.1 16.7=13.78 kN/m
n""g=0.75 1 0.62 16.7+0.75 0.08 1 22=9.0855 kN/m
272.888 kPa< 362,437 кПа, проходит по напряжениям - принимаем.
Section 3 -3
n"g=0.25 1 1.1 16.7=4.5925 kN/m
n""g=0.25 1 0.62 16.7+0.25 0.08 1 22=3.0285 kN/m
307.2028 kPa< 347,0977 кПа, проходит по напряжениям - принимаем.
Section 4-4
n"g= n""g=0.2 1 0.62 16.7+0.2 0.08 1 22=2.4228 kN/m
352.7268 kPa< 462,89 кПа, проходит по напряжениям - принимаем.
Section 5 -5
n"g=0.4 1 1.1 16.7= 7.348 kN/m
n""g=0.4 1 0.62 16.7+0.4 0.08 1 22=4.8456 kN/m
335.29 kPa< 359,0549 кПа, проходит по напряжениям - принимаем.
Section 6-6
n"g= n""g=0.2 1 0.62 16.7+0.2 0.08 1 22=2.43 kN/m
275.2525 kPa< 352,95кПа, проходит по напряжениям - принимаем.
DETERMINATION OF SOIL FOUNDATION SETTLEMENT BY LAYER-BY-LAYER SUMMARY METHOD
We consider the busiest section 2-2.
1. The thickness of the soil under the base of the foundation to a depth of at least 4b = 4 · 1.6 = 6.4 m is divided into elementary layers with a thickness of no more
hi = 0.4 b = 0.4·1.6=0.64 m.
- 2. Determine the distance from the base of the foundation to the upper boundary of each elementary layer zi (m).
- 3. Determine the stresses from the soil’s own weight acting at the level of the base of the foundation:
4. Determine the stress from the soil’s own weight at the lower boundary of each elementary layer using the formula:
5. Determine the stress from the soil’s own weight at the boundary of the main layers:
- 6. We construct stress diagrams from the soil’s own weight to the left of the foundation axis at the boundary of the main layers - .
- 7. We determine additional compressive stresses at the upper boundary of each elementary layer from the structure
where: p0 - additional pressure at the level of the base of the foundation
where: p - average actual pressure under the base of the foundation;
I - coefficient (Table 5.1 [1]),
where: - characterizes the shape and dimensions of the foundation base,
r - relative depth, .
8. We construct diagrams of additional stresses.
9. Determine the lower limit of the compressible thickness of the soil base. The point of intersection of diagrams and is taken as the lower boundary of the compressible thickness of the soil foundation.
To do this, we build a diagram to the right of the z-axis. Hc= m
10. Determine the average stress in elementary layers from the load of the structure:
11. We determine the amount of foundation settlement as the sum of the settlements of elementary layers:
where: n is the number of complete elementary layers included in the compressible thickness;
Si - elementary layer sediment
where: - dimensionless coefficient, =0.8;
hi is the thickness of the elementary layer;
Ei is the deformation modulus of the elementary layer;
срzpi is the voltage in the middle of the elementary layer.
The main condition for checking for deformation:
S = 5.1< SU = 10 см
Conclusion: settlement is acceptable.
Base settlement determination table
480 rub. | 150 UAH | $7.5 ", MOUSEOFF, FGCOLOR, "#FFFFCC",BGCOLOR, "#393939");" onMouseOut="return nd();"> Dissertation - 480 RUR, delivery 10 minutes, around the clock, seven days a week and holidays
Ivanov, Anton Andreevich. Assessment of the bearing capacity of foundations of slotted foundations based on an analysis of the stressed state of the soil mass and experimental data: dissertation... Candidate of Technical Sciences: 05.23.02 / Ivanov Anton Andreevich; [Place of protection: Volgogr. state architectural-builds. University].- Volgograd, 2013.- 164 p.: ill. RSL OD, 61 14-5/653
Introduction
Variable Design Parameters .
Formulation of goals and setting tasks
Determination of intervals of change in numerical values of variable design parameters used in calculating the bearing capacity of foundations of slotted foundations
Statement of the problem of the bearing capacity of a slotted foundation 12
Chapter II. Calculation of the bearing capacity of a slotted foundation based on an analysis of the stressed state of the soil at the base of its base using the method of complex potentials and experimental data 27
2.1. Some information about the method of complex potentials. Display function 27
2.2. Determination of display coefficients
functions 33
2.3. 48
2.4. Engineering method for calculating the bearing capacity of the base of a slotted foundation 60
Conclusions on Chapter II 65
Chapter III. Determination of the bearing capacity of a homogeneous base of a double-slit foundation
3.1. Mathematical research tools, description and characteristics of the mechanical and mathematical model and finite element calculation schemes for computer modeling of the process of formation and development of areas of plastic deformation 67
3.2. Analysis of the stress state of a homogeneous base of a double-slot foundation
3.3. Analysis of the development process of areas of plastic deformation in a homogeneous base of a double-slit foundation 77
3.4. Engineering method for calculating the bearing capacity of a homogeneous base of a double-slit foundation 83
Conclusions on Chapter III 96
Chapter IV. Experimental studies of the process of origination of areas of plastic deformation at the base of a slot foundation using models made of equivalent materials 98
4.1. Requirements for equivalent material and determination of its physical and mechanical properties 99
4.2. Experimental determination of the first critical load for the slot foundation model 103
Key findings 114
List of used literature
Introduction to the work
Relevance of the dissertation topic. The bearing capacity of the base of a slotted foundation consists of the bearing capacity along its base and along its side surface. In addition to the resistance forces caused by internal friction and adhesion of the soil, additional resistance forces act along the lateral surface and along the base of the foundation, arising due to: penetration of the water-colloidal cement mortar deep into the soil and its subsequent hardening with the formation of a thin soil-cement layer with crystalline bonds; expansion of concrete containing expansive Portland cement during hardening. The need to take these forces into account makes it necessary to improve methods for calculating the bearing capacity of slotted foundations. relevant .
Purpose of the dissertation research formulated as follows:
To develop an engineering method for calculating the bearing capacity of a slotted foundation, based on an analysis of the stressed state of the soil mass using the methods of the theory of complex variable and finite element functions and experimental determination of the total friction and adhesion forces between the side surface of the foundation and the enclosing soil mass directly on the construction site in real engineering-geological conditions .
To achieve this goal, it is necessary to solve the following tasks:
Conduct an analysis of existing methods for calculating the bearing capacity of the base of slotted foundations and technical literature, on the basis of which to determine the intervals of change in variable design parameters for conducting a numerical experiment.
Develop a mechanical and mathematical model and determine the numerical values of the coefficients of the mapping function that ensure conformal mapping of a half-plane with a cutout at predetermined values of the ratio of the width of its base to the depth (2b/h).
Carry out a computer simulation of the process of formation and development of areas of plastic deformation under the bottom of a slotted foundation, based on the results of which to obtain graphical dependencies and their analytical approximations that make it possible to determine the value of the design resistance and the maximum permissible load, provided that only the base of the foundation is taken into account. Develop a computer calculator program to automate this process.
To develop and obtain a title of title for a utility model of a device to determine in the field the total friction and adhesion forces acting along the contact “side surface of a slotted foundation - soil massif.”
To develop a mechanical and mathematical model and conduct computer modeling of the process of transformation of the stress state and the formation and development of areas of plastic deformation at the base of two slot foundations using the finite element method. Obtain graphical and analytical dependences of the dimensions of the OPD on the physical and mechanical properties of the soil, the dimensions of the foundation and the intensity of external influence. To propose an engineering method for calculating the bearing capacity of two slotted foundations, formalizing it in a computer program - a calculator.
Conduct experimental studies of the process of formation and development of areas of plastic deformation under the base of a slotted foundation, and compare the results obtained with the results of analytical studies.
To implement the results of the dissertation research into construction practice.
Reliability of results dissertation research, its conclusions and recommendations are justified:
Working hypotheses based on the fundamental principles of the linear theory of elasticity (methods of the theory of functions of a complex variable and finite elements), the theory of plasticity, engineering geology, soil science and soil mechanics;
Using verified computer programs registered in the state software register as tools for theoretical research;
Satisfactory convergence of the results of experiments to determine the critical loads for models of foundations of slotted foundations made of equivalent materials with the results of comparative calculations of real soil masses with adequate values of the coefficient of lateral soil pressure with the behavior of these objects in nature.
RF patent for utility model.
Scientific novelty of the dissertation work is that
The patterns of transformation of stress fields and the occurrence of the process of origin and development of areas of plastic deformation under the sole and along the contact “side surface of the slotted foundation - soil” during the loading of the foundation up to the achievement of critical loads have been established and studied;
Graphic dependences of the sizes (depth of development under the base and up along the foundation-soil contact) of areas of plastic deformation on the intensity of the external influence were constructed for all the numerical values of the variable design parameters considered in the dissertation for a double-slit foundation; analytical approximations of these dependencies formed a database of a computer calculator program for calculating the bearing capacity of a double-slit foundation;
To determine the bearing capacity of the bottom of a slotted foundation, methods of the theory of functions of a complex variable were used, which made it possible to completely exclude the lateral surface of the slotted foundation from consideration;
To determine the bearing capacity of the side surface of a slotted foundation, a utility model of a device has been developed and patented for determining the total friction and adhesion forces arising at the contact “side surface of a slotted foundation - soil” when pouring concrete without formwork;
An engineering method has been developed for calculating the bearing capacity of the base of a slotted foundation, based on the use of a patented device and a computer calculator program for calculating the bearing capacity of the base of a slotted foundation;
Practical significance of the work . The dissertation work is part of scientific research conducted at the departments of “Applied Mathematics and Computer Science” and “Hydraulic Engineering and Earthworks” of Volga State University of Civil Engineering in 2010-2013.
The results obtained while working on the dissertation can be used for :
calculating the bearing capacity of the base of a slotted foundation with a wide range of changes in the numerical values of variable design parameters, including the geometric dimensions of the foundation and the physical and mechanical characteristics of the foundation soils;
experimental determination directly at the construction site of the total friction and adhesion forces that arise along its lateral surface when concreting the foundation body by surprise without formwork;
calculating the bearing capacity of the base of a double-slit foundation for various values of its geometric dimensions and physical and mechanical characteristics of the enclosing soil mass;
preliminary assessment of the bearing capacity of foundations of slotted foundations at the preliminary design stage;
assessing the possible error in calculating the bearing capacity on the side surface of a slotted foundation using known methods using a device patented by the author.
Approbation of work. The main results of the research carried out by the author of the dissertation work were reported, discussed and published in the materials of: annual scientific and technical conferences of teachers, graduate students and students of the Volgograd State University of Architecture and Civil Engineering (Volgograd, VolgGASU, 2010-2013), the All-Russian Scientific and Technical Conference “Soil mechanics in geotechnics and foundation engineering” (Novocherkassk, SRSTU-NPI, 2012); III International Scientific and Technical Conference “Engineering Problems of Building Materials Science, Geotechnical and Road Construction” (Volgograd, VolgGASU, 2012); All-Ukrainian scientific and practical seminar with the participation of foreign specialists “Modern problems of geotechnics” (Ukraine, Poltava, PNTU named after Yu. Kondratyuk, 2012); at scientific seminars of the departments “Applied Mathematics and Computer Science” and “Hydraulic Engineering and Earthworks” of VolgGASU (Volgograd, VolgGASU, 2010-2013).
development and compilation of mechanical and mathematical models and calculation schemes of methods of the theory of functions of a complex variable and FEM of the objects under study (coefficients of the mapping function, boundary conditions, dimensions, type, degree of discretization);
carrying out computer modeling of the processes of formation and development of areas of plastic deformation in the bases of slot and double-slot foundations, processing, analyzing and systematizing the results obtained, constructing graphical dependencies and their analytical description;
conducting a patent search, analyzing its results, developing a utility model and patenting it;
development of engineering methods for calculating the bearing capacity of slotted and double-slit foundations;
formation of databases and development of computer calculator programs designed to assess the bearing capacity of slotted foundations;
implementation of the results of the dissertation work into construction practice at the design stage.
Submitted for defense :
Mechanical and mathematical models and calculation schemes of methods of the theory of functions of a complex variable and the finite element method of the objects under study.
Established patterns of the process of formation and development of areas of plastic deformation under the soles and along the side surface of slotted foundations.
A technique for excluding the side surface of a slotted foundation from consideration based on the use of methods from the theory of functions of a complex variable.
A useful model of a device for determining the total friction and adhesion forces arising at the contact “side surface of a slotted foundation - soil” when pouring concreting without formwork;
An engineering method for calculating the bearing capacity of a slotted foundation and a computer calculator program for determining the bearing capacity of its lateral surface.
An engineering method for calculating the bearing capacity of a double-slot foundation and a computer program-calculator that formalizes it.
Results of implementing the results of the dissertation work into construction practice.
The results of scientific research are implemented:
When determining the bearing capacity of the base of monolithic foundations made against the soil at the site: “Canteen building on the street. Barrikadnaya, house 11, in the village. Red Barricades of the Ikryaninsky district of the Astrakhan region" at LLC NPF Engineering Center "YUGSTROY".
When developing projects and constructing the underground part of buildings and structures erected using the “wall in soil” technology, in particular: when designing the administrative complex “Business Park” in the city of Perm, fencing the coastal zone of an artificial island in the water area of the river. Kama (Perm region).
In the educational process at the department of “Hydraulic and Earthworks” of the Volgograd State University of Architecture and Civil Engineering.
Publications . The main provisions of the dissertation were published in 8 scientific articles, two of them in leading peer-reviewed scientific publications and 1 Russian Federation patent for a utility model.
Structure and scope of work . The dissertation consists of an introduction, four chapters, general conclusions, a list of references of 113 titles and appendices. The total volume of work is 164 pages of typewritten text, including 114 pages of main text containing 145 illustrations and 14 tables.
Features of the technology of construction, operation and calculation of the bearing capacity of slotted foundations in cohesive soils
Typically, the development of pits and trenches for columnar and strip prefabricated foundations is carried out by an excavator, followed by manual cleaning of the bottom and side surfaces. Therefore, for these foundations, the calculated payload is transferred to the soil foundation only through their base. The soil resistance of the backfill is not taken into account in the calculation.
On the contrary, in soils of natural composition, especially low-moisture cohesive soils, the use of monolithic slot foundations with a developed lateral working surface is very promising. When constructing such foundations, there is no need to backfill trenches and pits, which allows for the emergence of significant friction and adhesion forces between the soil mass, which is not possible when constructing conventional foundations in open pits.
High efficiency of application is shown by slotted foundations, which are one or a system of parallel narrow cracks in the ground, filled in space with concrete, which are combined by a grillage into a common foundation to absorb the load from the above-ground part of the building. The construction of slots can be carried out by cutting them with a drill or a slot cutter, and in the case of a large depth of the slot foundation, it can be constructed using the “wall in soil” method.
The external load is transmitted to the soil base along the side surface of the slotted foundation, along the base and along the base of the grillage slab, if any.
In the case of combining two or more slotted foundations into a single foundation, the soil mass enclosed between the walls is also included in the work, due to which the load is transmitted in a plane at the level of the lower ends of the walls.
The bearing capacity of such a foundation depends significantly on the distance between the walls. In this case, the soil enclosed between the walls, the walls themselves and the grillage together can be considered as a concrete-soil foundation on a natural foundation, the height of which is equal to the height of the walls. If any part of the external load is transmitted by the outer walls, then this circumstance leads to an increase in the width of the conventional concrete-soil foundation that transfers the loads to the foundation soils.
Particular attention should be paid to the issue of load transfer along the side surface of an isolated slot foundation. The work states that slotted foundations based on the bearing capacity of the foundation soils should be calculated based on the expression N Fdlyk, (1.1) where: Fd is the bearing capacity of the foundation soil; y =1.2, if the bearing capacity of the foundation is determined by the results of field tests in accordance with GOST and y =1.4, if the bearing capacity is determined by calculation; N is the design load transferred to the foundation, kN. The bearing capacity of a slotted foundation (SF) of rectangular cross-section, operating on a central axial compressive load and resting on a compressible base, if its lateral surface intersects several parallel layers of foundation soil, can be determined by the formula: where: ус=1 - condition coefficient foundation work; usg - coefficient of working conditions of the pound under the base of the foundation, taking the value 1.0; 0.9; 0.4 when developing a trench dry with a backhoe bucket, when developing a trench with a flat bucket bucket dry or under a clay solution with removal of sludge from the bottom of the trench, and when developing a trench with a flat paddle bucket under a clay solution without removing sludge from the bottom of the trench, respectively; R is the calculated resistance of a pound under the base of the foundation, (kPa), taken according to table No. 3.1 (page 63); A - area of the foundation base, (m); U - foundation perimeter, (m); yct is the coefficient of operating conditions of the pound along the lateral surface of the foundation, taking the value 0.8; 0.7 and 0.6 when concreting a trench dry in loams, clays and when concreting a trench under the protection of a clay solution for all soils, respectively, or is specified experimentally; /I - the calculated resistance of the ith layer of pound on the side surface of the slotted foundation, (kPa), taken according to table No. 3.2 (p. 63), but not more than bOkPa; h\ is the thickness of the i-th pound layer in contact with the side surface of the slot foundation, (m).
Similar formulas and tables are given in documents developed at the NIIOSP named after. N.M. Gersevanova. Formula (1.2) itself looks convincing and its use is quite logical. From this formula it is clear that the payload transmitted by the slotted foundation to the foundation is divided into two parts: the first part is transmitted through the base of the foundation, and the second through its side surface. Special and regulatory literature provides data on the fractional distribution of the bearing capacity of slotted foundations along their base and side surface.
Computer modeling of the process of origin and development of areas of plastic deformation in the foundation under the bottom of a slotted foundation
Returning to consideration of Fig. 2.6, we see that the proposed technique gives adequate results: the isolines of normal az and ax stresses at some distance from the cutout become parallel to the day surface of the soil massif; the ratio of the numerical values of these stresses at the corresponding points, approximately, as it should be, is equal to the value of the coefficient of lateral soil pressure (aJoz ", =0.75); the isolines of tangential stresses tgx have the classic “butterfly” shape, their numerical values at points lying on the symmetry axis of the design scheme are equal to zero.
Computer modeling of the process of origin and development of areas of plastic deformation in the foundation under the bottom of a slotted foundation
Before the start of the study, numerous literary sources were reviewed, in particular, works, and according to the data presented in them, it was established that the depth of laying slot foundations can vary in the range of 2m h 43m, and the most typical values of the ratio of the width of the slot foundation to the depth of its laying are 2Mz = 0.03;0.13;0.27;0.4.
According to the data presented in the first chapter of the dissertation, which are based on the results of an analysis of regulatory documentation and literary sources, the strength characteristics of cohesive soil vary within the following limits: angle of internal friction p = kPa.
Taking these circumstances into account, it turned out that the value of the reduced connectivity pressure, calculated by the formula from - C(yhtg(p) \ varies in the interval ссв = .
In order for the mapping function (2.5) to provide a mathematical model of the foundation of a slotted foundation with a wide range of numerical values for the ratio of the width of the foundation to its depth 2b/h, we will use the numerical values of the coefficients of the mapping function (2.6) given in Table No. 2.5.
Calculations to determine the value of the design resistance of the base of a slotted foundation were performed using computer programs ASV32 and “Stability. (Stress-strain state)" developed at the Volgograd State
Areas of plastic deformation at the base of a slot foundation during inception (a), development (b) and at the moment of reaching the maximum permissible load (closing of the maximum permissible load) (c) University of Architecture and Civil Engineering, for all possible combinations of numerical values of variable design parameters 2b/h, osv and f. In Fig. 2.10 shows, as an example, areas of plastic deformations at the base of a slotted foundation during their initiation, development, and at the moment of reaching the maximum permissible load (closing of the maximum permissible load).
In Fig. 2.11 shows, as the most obvious, graphical dependencies of the form AZ=J, AZe.
According to the limits adopted in Chapter I for changing the numerical values of variable design parameters, in order to achieve the goal set in the dissertation work, it is necessary to perform 1024 computational operations to determine the size of areas of plastic deformation at the base of a double-slot foundation.
The result of this chapter should be an engineering method for calculating the bearing capacity of a homogeneous base of a double-slot foundation, developed on the basis of the results of an analysis of its stress state and the process of formation and development of areas of plastic deformation in the active zone of the foundation.
Below in Fig. 3.3 3.5 pictures of dimensionless isolines (in fractions of y/g) of three stress components az are presented; ax and tzx in a homogeneous base of double-slot foundations of various widths (2/ =0.8/g; 0.4/?; 0), having the same depth, at the moment of closure of plastic deformation areas, that is, at the moment the intensity of the external uniformly distributed load of its maximum permissible value (or at the moment of loss of stability of the base). Note that in the latter case, at L=0 (see Fig. 3.2), the double-slot foundation degenerates into a single-slot (or simply slot foundation) of double width.
Experimental determination of the first critical load for the slot foundation model
The external dimensions of the form are 30x30 cm, and its width is 3.4 cm. Internal dimensions are 28x28 cm and 2 cm, respectively. The form is made of plexiglass 7mm thick, and its elements are fastened together with 13 metal bolts. Inserts-stamps made of organic glass, representing 105 models of slotted foundations, are made with a height of 15 cm, a width of 1.2 cm and a thickness of 2 cm, i.e. the last size is equal to the thickness of the model being manufactured. The models were formed with a variable cutting depth so that it was possible to simulate a slot foundation with a ratio of its width to the depth of foundation 2Mz3=0,l; 0.15; 0.2; 0.25 and 0.3.
The part of the insert-stamp located above the surface of the model serves to support the DOSM-3-1 dynamometer, which measures the magnitude of the force transmitted to the base model, created by a vertically located screw.
Before the experiment, the entire insert-stamp was carefully lubricated with technical petroleum jelly to eliminate the influence of friction forces.
The essence of the experiment was as follows.
From gelatin-gel CS with gelatin weight concentration equal to 15%, 30% and 45%, four batches of five models of slotted foundation bases were sequentially produced (Fig. 4.2a), with a width ratio of 2&/A3=0.l;0.15 ; 0.2; and 0.3.
Then these models were loaded through the stamp insert with a vertical, evenly distributed load until tiny cracks began to be clearly visible at the lower edges of the stamp insert - a sign of the beginning of destruction (Fig. 4.4). The corresponding load values were recorded and taken as the value at which limit state areas begin to form in the material of the slot foundation model, i.e. for the value of the first critical load.
The arithmetic mean of five (for each batch of models with the same value of 2b/h3) value q3 was taken as the result of the experiment for this batch. Five such experimental values were obtained; they are presented in table No. 4.2.
The same table shows the values of the corresponding loads obtained on the basis of calculations performed using the computer program “Stability. Stress-strain state”, developed at VolgGASU. Note that all calculations were carried out at a lateral pressure coefficient of pound = 0.75, which is the average value for clay soils.
Graphic interpretation of experimental and theoretical data in the form of dependencies like q3=f and the finite element method.
Comparing the areas of plastic deformations constructed on the basis of the calculation results (Fig. 4.6) for the moment of their initiation, and the OPD for this case under consideration, shown in Fig. 4.6c, we see their practical identity. opd- Fig. 4.6. Areas of plastic deformation at the base of the slot foundation model, constructed from stresses calculated using MTFKP (a; b) and using the finite element method (c)
Consequently, it can be argued that the obtained experimental data coincide with the data obtained by calculation with a degree of accuracy sufficient for engineering practice. This gives reason to believe that the engineering method for calculating the bearing capacity of a slotted foundation developed at VolgGASU can be recommended for practical use.
1. The bearing capacity of a slotted foundation on the ground is determined by the sum of the bearing capacity on the side surface and its base. The first term is determined by the physical and mechanical properties of the enclosing soil mass, the hydro-geological conditions of the construction site, the geometric dimensions of the foundation, the physical and chemical properties of concrete, the degree of penetration of the colloidal water-cement solution into the surface layers of the soil of the pit (trench) slopes, the technology of foundation construction, and so on. The second term depends on the shape and size of the sole and FMSG. Therefore, it is possible to determine the bearing capacity along the base of the foundation based on the analysis of the stress-strain state of the soil mass using FEM and MTFKP, and the bearing capacity along the lateral surface - through experimental studies directly at the construction site.
2. Based on the methods of the theory of functions of a complex variable, graphical dependencies and corresponding analytical approximations are obtained, which make it possible to determine the bearing capacity along the base of a slotted foundation for all possible combinations of numerical values of the design parameters used in the dissertation work. These results formed a database of a computer calculator program that allows you to automate the process of calculating the part of the bearing capacity attributable to the base of the foundation.
3. A device has been developed and patented that allows, in real engineering-geological conditions of a specific construction site, to determine the maximum values of the specific friction and adhesion forces acting on the lateral surface of monolithic foundations manufactured without formwork against the soil.
To calculate the settlement of the foundation and check the strength (bearing capacity) of the foundation, you need to know the stress distribution in the foundation, i.e. its stressed state. It is necessary to have information about the distribution of stresses not only along the base of the foundation, but also below it, since the settlement of the foundation is a consequence of the deformation of the soil layer located underneath it. To calculate the bearing capacity of the foundation, it is also necessary to determine the stresses in the soil below the base of the foundation. Without this, it is impossible to establish the presence and size of shift areas, check the strength of the soft soil layer, etc.
To theoretically determine the stresses in the foundation, as a rule, solutions of the theory of elasticity obtained for a linearly deformable homogeneous body are used. In reality, soil is neither a linearly deformable body, since its deformations are not directly proportional to pressure, nor a homogeneous body, since its density changes with depth. However, these two circumstances do not significantly affect the distribution of stresses in the base.
This chapter does not discuss all issues of the stressed state of foundations, but only the methodology for determining the normal stresses acting in the soil along horizontal areas.
§ 12. Distribution of stresses along the base of the foundation
In bridge and hydraulic engineering construction, as a rule, rigid foundations are used, the deformations of which can be neglected, since they are small compared to the movements associated with settlement.
Measurements of normal stresses (pressures) along the base of the foundation, carried out using special instruments mounted at the level of the base, showed that these stresses are distributed according to a curvilinear law, depending on the shape and size of the foundation in plan, soil properties, average pressure on the base and other factors .
Rice. 2.1. Actual and theoretical diagrams of normal stresses along the base of the foundation
As an example in Fig. 2.1, the solid line shows the actual distribution of normal stresses (normal stress diagram) along the base of the foundation when the load (force N) is significantly less than the bearing capacity of the foundation, and the dotted line shows the stress distribution obtained on the basis of solutions from the theory of elasticity.
At present, despite the accumulated experimental material and theoretical studies, it is not possible to establish in each specific case the actual pressure distribution along the base of the foundation. In this regard, practical calculations are based on straight-line pressure diagrams.
Rice. 2.2. Straight-line diagrams of normal stresses along the base of the foundation a - under central compression; b- with eccentric compression and e W/A
With central compression (Fig. 2.2, a), the stresses Pm, kPa, along the base are assumed to be uniformly distributed and equal:
Pm = N/A, (2.1)
where N is the normal force in the section along the base of the foundation, kN; A is the area of the foundation base, m2.
With eccentric compression, the stress diagram is taken in the form of a trapezoid (Fig. 2.2, b) or a triangle (Fig. 2.2, c). In the first of these cases, the highest voltage and the lowest voltage Pmin are determined by the expressions:
Pmax = N/A + M/W;
Pmin = N/A - M/W (2.2)
where M - Ne is the bending moment in the section along the base of the foundation, kN m (here e is the eccentricity of the application of force N, m); W is the moment of resistance of the area of the foundation base, m 3.
Formulas (2.2) are valid in cases where the bending moment acts in a vertical plane passing through the main central axis of inertia of the foundation base.
With the base of the foundation in the form of a rectangle with a size perpendicular to the plane of action of the moment M, b and another size a, we have A = ab and W = ba2/6. Substituting expressions A and W into formulas (2.2) and taking into account that M = Ne, we obtain:
Pmax =N/ba(1+6e/a)
Pmin=N/ba(1-6e/a) (2.3)
The stress Pmin, kPa, calculated by formula (2.2) or (2.3) at eccentricity e> W/A, turns out to be negative (tensile). Meanwhile, in the section along the base of the foundation, such stresses practically cannot exist. When e> W/A, the edge of the base of the foundation, which is more distant from the force N, rises under the influence of this force above the ground. In a certain area of the base of the foundation (from this edge), the contact between the foundation and the soil is broken (the so-called detachment of the foundation from the soil occurs), and therefore the stress diagram P has the form of a triangle (see Fig. 2.2, c). Formulas (2.2) and (2.3) do not take this circumstance into account, therefore they cannot be used for e> W/A.
Formulas for determining the size a 1, m, part of the base along which the contact of the foundation with the ground is maintained, and the highest stress Pmax, kPa (see Fig. 2.2, c) can be obtained by taking into account that the stresses P must balance the force N, kN acting at a distance c from the edge of the foundation base closest to this force.
This implies two conditions: 1) the center of gravity of the stress diagram P is located on the line of action of the force N; 2) the volume of the diagram is equal to the magnitude of this force. From the first condition with a rectangular base of the foundation it follows
A1=3c, (2.4)
and from the second
(Pmax a 1 /2)b = N. (2.5)
From formulas (2.4) and (2.5) we obtain
Pmax =2N/(3cb). (2.6)
So, at eccentricity e> W/A = a/6, the maximum pressure along the rectangular base of the foundation Pmax should be determined by formula (2.6).
Let us consider, as an example, the calculation of an eccentrically loaded free-standing foundation (see diagram with the main accepted notations).
All forces acting along the edge of the foundation are reduced to three components in the plane of the base of the foundation N, T, M.
Calculation actions are performed in the following sequence:
1. We determine the components N, T, M, which can be written in the most general case as:
2. Having determined the dimensions of the foundation, as for a centrally loaded foundation - (I approximation), and knowing its area - A, we find its edge stresses P max, min. (We assume that the foundation is stable for shear).
From the resistance of materials for structures experiencing compression with bending it is known that: 
For a rectangular foundation, the sole can be written:
Then, substituting the accepted notation into the strength of strength formula, we obtain:
Where ℓ is the larger size of the foundation (the side of the foundation in the plane of which the moment acts).
- based on the calculation data, it is not difficult to construct diagrams of contact stresses under the base of the foundation, which are generally presented in the diagram.
According to SNiP, restrictions have been introduced on the values of edge stresses:
- P min / P max ≥ 0.25 - in the presence of a crane load.
- P min / P max ≥ 0 - for all foundations, i.e. tearing off the sole is unacceptable.
In graphical form, these stress restrictions under the base of an eccentrically loaded foundation (1, 2) do not allow the use of the last two diagrams of contact stresses shown in the diagram. In such cases, a recalculation of the foundation with a change in its dimensions is required.
It should be noted that R is determined based on the condition of development of plastic deformation zones on both sides of the foundation, while in the presence of eccentricity (e), plastic deformations will form on one side. Therefore, a third limitation is introduced:
- P max ≤1.2R - while P av ≤ R.
If the base of the foundation is torn off, i.e. Р min< 0, то такие условия работы основания не допустимы (см. нижний рисунок). В этом случае рекомендуется уменьшить эксцентриситет методом проектирования несимметричного фундамента (смещение подошвы фундамента).
Sections
Permanent address for this chapter: website/learning/basesandfoundations/Open.aspx?id=Chapter3The purpose of the calculation is to determine the average. Maximum and minimum stress under the base of the foundation and compare them with the calculated soil resistance.
Where P, P max and P min are, respectively, the average, maximum and minimum pressure of the base of the foundation on the base;
N 1 - calculated vertical load on the base, taking into account hydrostatic pressure, if any;
M 1 - design moment relative to the axis passing through the center of gravity of the foundation base;
A – area of the sole;
W – moment of resistance along the base of the foundation;
y с - coefficient of working conditions is assumed to be 1.2;
y n - reliability coefficient for the purpose of the structure, taken equal to 1.4;
l - length of the base of the foundation
b- width of the foundation base
R - calculated soil resistance under the base of the foundation
The calculated vertical load on the base is determined by the formula:
N 1 =1.1*(p o +p p +p f +p in +p g)*y ƒ *p k,
Where p f and r g are the loads from the weight of the foundation and the soil on its ledges, mN;
p in - load from the weight of water acting on the ledges of the foundation (taken into account if the foundation is embedded in waterproof soil), mN;
p p - weight of the span, mN;
r k - silt acting from a temporary vertical moving load, mN;
p o - support weight, mN.
N 1 =1.1*(4.3+1.49)+1.13*6.6=13.00 mN
The moment of resistance at the base of the foundation will be equal to:
W=W= 
The design moment about the axis passing through the center of gravity of the foundation base will be equal to:
M 1 =1.1*T*(1.1+h 0 +h f)=1.1*0.66*(1.1+6.4+3.5)=7.98mN*m
Now let’s check whether the stress condition under the base of the foundation is satisfied:
P max = 
P min = 
P max = 
P= - executed
Р max = - executed
P min = - executed
All three conditions for stress strength under the base of the foundation are met, therefore, the calculation was performed correctly.
3.5 Calculation of foundation settlement
,Where
Dimensionless coefficient equal to 0.8;
G zpi is the average vertical (additional) stress in the i-th soil layer;
h i and E i are the thickness and deformation modulus of the i-th soil layer, respectively:
n is the number of layers into which the compressible thickness of the base is divided.
The calculation technique comes down to the following:
1. The compressible thickness of the soil located below the base of the foundation is divided into elementary layers of thickness h i, where b is the width of the base of the foundation = 5.44 m. The thickness of the layer is assumed to be h i = 2.0 m.
The boundaries of elementary layers must coincide with the boundaries of soil layers and the groundwater level.
The depth of the layout should be approximately 3* b=3*5.44=16.3m
Divide into 10 layers. The calculation data is entered into table 2.
2. Determine the values of vertical stresses from the soil’s own weight at the level of the base of the foundation and at the boundary of each sublayer
Vertical stress from the soil's own weight at the level of the base of the foundation
,
Where K k is the geostatic coefficient of lateral pressure, equal to 1;
z i =h f - depth of the foundation base (z i =3.5)
y – specific gravity of soil below the groundwater level (determined taking into account the weighing effect of water) y sb = 10 kN/m 2
From here: 
kPa
z i is the distance from the base of the calculation layer to the base of the foundation;
y i is the specific gravity of soils of the i-th layer. The specific gravity of soils lying below the groundwater level or below the water in the river, but above the aquitard, must be determined taking into account the weighing effect of water: In an aquitard, the stress from the own weight of the soil in any horizontal section without taking into account the weighing effect of water.
We determine the values of vertical stresses from the soil’s own weight at the boundary of each sublayer (we enter the data in the table). Based on the calculation results, we construct a diagram of vertical stresses from the soil’s own weight.
3. We determine additional to the natural vertical stress under the base of the foundation using the formula:
P - average pressure on the ground from standard constant loads
A – area of the base of the foundation,
N 11 - design vertical force
N 11= р 0 +р n +р g +р in, where
p 0 - support weight;
p n - weight of the span;
r g - load from the weight of the soil on its ledges;
p in - load from the weight of water acting on the ledges of the foundation (taken into account if the foundation is cut into waterproof soil)
N 11 =4.3+1.49+5.6=11.39*10 3 =11390kN
P= 
kN/m 2
The ordinate value of the distribution diagram of additional vertical stresses in the soil is calculated using the formula:
Coefficient taken from the table depending on the shape of the foundation base.
Aspect ratio of a rectangular foundation
and relative depth equal to
We find the coefficient from the table and calculate the ordinate values of the diagram of the distribution of additional vertical stresses in the soil.
| Calc. layer | Layer No. | Layer thickness, h, m | z i , m | kPa | γ i, kN/m 3 | 0.2 | 2z/b | E 1 | S i | ||||
| kPa | kPa | ||||||||||||
| clay | 2,8 | 10,0 | 7,0 | 142,38 | 137,19 | 13.000 | 0,057 | ||||||
| clay | 1,5 | 1,5 | 10,0 | 0.60 | 0,927 | 132,0 | 114,63 | 20.000 | 0,025 | ||||
| 2,0 | 3,5 | 10,0 | 1,29 | 0,683 | 97,25 | 85,43 | 0,013 | ||||||
| 2.0 | 5,5 | 10,0 | 2,02 | 0,517 | 73,61 | 62,93 | 0,009 | ||||||
| 2.0 | 7,5 | 10,0 | 2,78 | 0,367 | 52,25 | 50,33 | 0,003 | ||||||
| Fine sand | 0,9 | 8,4 | 10,0 | 23,8 | 3,09 | 0,340 | 48,41 | 40,65 | 37.000 | 0,002 | |||
| 2,0 | 10,4 | 10.0 | 27,8 | 3,82 | 0,231 | 32,90 | 29,48 | 0,002 | |||||
| 2,0 | 12,4 | 10,0 | 31,8 | 4,56 | 0,183 | 26,06 | 24,14 | 0,002 | |||||
| 2,0 | 14,4 | 10.0 | 35,8 | 5,30 | 0,156 | 22,21 | 20,43 | 0,001 | |||||
| 0.6 | 15,0 | 10,0 | 37,0 | 5,52 | 0,138 | 19,65 | Total: | 0,114 |
4. Determine the lower boundary of the compressible thickness (BC). It is located on a horizontal plane where the condition is met.