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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 foundation 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-slot 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 of 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 occurrence 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 (p. 63); A - area of the foundation base, (m); U - foundation perimeter, (m); yct is the coefficient of operating conditions of the pound along the side 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 characteristic 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 with 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 the 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.
We calculate the stresses acting along the base of the foundation using formulas (4.1) – (4.3). We present the calculations in tabular form (Table 1).
In table 1 γ f = 1.1 – safety factor for load to wall weight;
γ f = 1.2 – the same, to the active soil pressure.
Table 1
| Standard force, kN | Design force, kN | Shoulder, m | Moment, kNm |
| G st = . . (6 – 1.5) . 24 = 175 | G st = 1,1 . 175 = 192,5 | 0,1 | - 19,3 |
| G f = (1.5.3 -.24 = 103.3 | G f= 1,1 . 103,3 = 113,6 | 0,05 | + 5,7 |
| E ag = 267.8 | E ag =1.2. 267.8 = 321.4 | 2,4 | + 771,3 |
| E av = 51,3 | E A V = 1,2 . 51,3 = 61,6 | 1,15 | - 73,9 |
| E n = 18.5 | E n = 1. 18.5 = 18.5 | 0,5 | - 9,3 |
Linear scale: 1 ¸…..
Pressure scale: 1…..
Rice. 9 Construction of Poncelet. Calculation example
We calculate the moments relative to the axes passing through the center of gravity of the foundation base (point O in Fig. 10). Resultants of active and passive E n We apply pressure to the wall at the level of the center of gravity of the pressure intensity diagrams. The weight of the wall and foundation is at the center of gravity of the corresponding element.
The arms of forces can be taken to scale according to the drawing or found analytically.
Sum of calculated vertical forces N 1 = 192.5 + 113.6 + 61.6 = 367.7 kN.
Sum of moments of design forces M 1= - 19.3 + 5.7 + 771.3 – 73.9 - 9.3 = 674.5 kNm.
Area and moment of resistance of the base of the wall foundation according to formulas (4.4) and (4.5)
A = b . 1 = 3 . 1 = 3 m2;
W = = 1.5 m 3.
p avg= = = 122.6 kPa;
р ma x = 572.3 kPa, р min =- 327.1 kPa.
Rice. 10. Cross section of the wall, forces acting on it, and stress diagram along the base of the foundation
Stress diagrams along the base of the wall are shown in Fig. 10.
Let's compare the found voltages with the calculated resistance:
p av = 122,6 < = 631,4 кПа;
p m ax = 572,3 < = 757,7 кПа;
р min =- 327,1 < 0
Of the three conditions, the last one is not met, i.e. Tensile stresses act along the back edge of the sole, which is not allowed.
Calculation of wall stability against overturning and shifting along the base of the foundation
The calculation of stability against capsizing is carried out in accordance with formula (4.7). We calculate the holding and overturning moments in tabular form (Table 2).
table 2
In table 2 moments are calculated relative to the front face of the wall foundation (point O 1 in Fig. 10), γ f = 0.9 is the safety factor for the load to the weight of the wall.
1,38 > = 0,73,
those. condition (4.7.) is not satisfied.
Calculation of the stability of the wall against shear along the base of the foundation is carried out in accordance with formula (4.8) using the data
Shear force r 1 = E ag – E p = 321.4 – 18.5 = 302.9 kN.
Holding force z 1 = Ψ (G c t + G f + E aw) = 0.3 . (157.5 + 93 + 61.6) = 93.6 kN.
Here Ψ = 0.3 is the coefficient of friction of the masonry on the ground (Table 8, Appendix 2):
3,24 > = 0,82,
those. condition (4.8) is not satisfied.
Checking the position of the resultant
Calculation of M II and N II is carried out according to formula (4.9) with load safety factors = 1 using the data from table. 1.
Eccentricity
e 0 = = = 1.68 m;
0.5 m;
3,36 > = 0,8
those. and this check is not performed.
The checks performed showed that the retaining wall given in the assignment does not meet most of the requirements set by the building regulations. The wall needs to be redesigned. There are several ways to achieve compliance with the requirements of the standards:
Increase the width of the base of the wall;
Change the slope and increase the roughness of the back face of the wall;
Make the wall more massive;
Reduce the active pressure by replacing the backfill with soil with a large angle of internal friction, etc.
APPLICATIONS
Coursework assignment
"Calculation of a retaining wall"
Explanations for choosing a task
The teacher gives the student a four-digit assignment code.
The first number indicates the option of wall dimensions (Table 1).
The second is a variant of the backfill soil characteristics (Table 2).
The third is a variant of the characteristics of the soil lying under the base of the foundation (Table 3).
The fourth option is a uniformly distributed load on the surface of the backfill (Table 4).
For example, a student is given the code 1234. This means that the student, according to the table. 1 takes = 1 m; b = 3 m, etc.; according to table 2 γ сс = 19 ; φ = 29 degrees, etc.; according to table 3 soil – coarse sand, γ сс = 19.8; ω = 0.1, etc.; according to table 4 q = 50 kPa.
In Fig. Figure 11 shows the cross-section of the retaining wall with letter designations of dimensions, the values of which should be taken from the table. 1.
Rice. 11. Cross section of a retaining wall
Initial data for course work
Table 1
Wall dimensions
| Name | Designations | Dimension | Options | |||||||||
| Top width | m | 1,2 | 1,4 | 1,6 | 0,8 | 1,0 | 1,2 | 1,4 | 1,4 | 1,6 | ||
| Outsole width | b | m | 5,5 | 2,5 | 3,5 | 4,5 | 5,5 | 3,5 | 4,5 | |||
| Height | N | m | ||||||||||
| Laying depth | d | m | 1,5 | 2,5 | 1,5 | 2,5 | 1,5 | |||||
| Rear slope | ε | hail | - 2 | - 4 | -6 | -8 |
Backfill soil characteristics
table 2
| Name | Designations | Dimension | Options | |||||||||
| Specific gravity | γ zas | kN/m 3 | ||||||||||
| Angle of internal friction | φ | hail | ||||||||||
| Angle of soil friction against the back face of the wall | hail | |||||||||||
| Backfill surface slope | hail | - 2 | - 4 | - 6 | - 8 | - 10 |
Characteristics of the soil under the base of the wall foundation
Table 3
| Name | Designations | Dimension | Options | |||||||||
| Priming | - | - | fine sand | coarse sand | sandy loam | loam | clay | |||||
| Specific gravity | γ | kN/m 3 | 18,5 | 19,2 | 19,8 | 19,0 | 20,2 | 20,1 | 18,3 | 21,4 | 21,0 | 21,8 |
| Humidity | - | 0,2 | 0,23 | 0,1 | 0,19 | 0,2 | 0,2 | 0,45 | 0,16 | 0,14 | ||
| Specific gravity of solid particles | γs | kN/m 3 | 26,4 | 26,6 | 26,8 | 26,5 | 26,7 | 26,8 | 26,0 | 27,3 | 27,5 | 27,6 |
| Yield strength | - | - | - | - | - | 0,24 | 0,24 | 0,54 | 0,24 | 0,33 | 0,34 | |
| Rolling limit | - | - | - | - | - | 0,19 | 0,19 | 0,38 | 0,14 | 0,15 | 0,16 |
Table 4
The assignment contains only those initial data that correspond to the code received from the teacher.
The retaining wall is drawn to scale in accordance with the specified dimensions.
The retaining wall design assignment does not replace the title page of the course work.
Design example
State educational institution of higher professional education
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=Chapter3Where b- dimensionless coefficient equal to 0.8;
szp,i i th layer of soil from pressure along the base of the foundation pII, equal to half the sum of the indicated voltages at the top zi- 1 and bottom zi
szу,i- average value of vertical normal stress in i th layer of soil from its own weight selected when excavating a foundation pit, equal to half the sum of the indicated stresses on the top zi- 1 and bottom zi the boundaries of the layer vertically passing through the center of the base of the foundation;
hi And Еi- thickness and deformation modulus, respectively i- th layer of soil;
Eei- deformation modulus i- th layer of soil along the branch of the secondary load (in the absence of data, it is allowed to take equal Eei= = 5Еi);
n- the number of layers into which the compressible thickness of the base is divided.
In this case, the distribution of vertical normal stresses along the depth of the foundation is taken in accordance with the diagram shown in Figure 15.
z from the base of the foundation: szp And szу,i– vertically passing through the center of the base of the foundation, and szp,c– vertically passing through the corner point of a rectangular foundation, determined by the formulas:
Where a- coefficient taken according to Table 17 depending on the shape of the foundation base, the aspect ratio of the rectangular foundation and the relative depth equal to: x (x=2z/b– when determining szp And x=z/b– when determining szp,s);
pII- average pressure under the base of the foundation;
szg,0 - at the level of the base of the foundation (when planning, cutting is taken szg, 0 = d, in the absence of planning and planning with bedding szg, 0 = = dn, Where - specific gravity of the soil located above the base, d And dn– indicated in Figure 15).
Vertical stress from the soil's own weight szg z from the base of the foundation, determined by the formula
| , | (35) |
where is the specific gravity of the soil located above the base of the foundation (see clause 3.2);
dn- depth of foundation from natural mark (see Figure 15);
gIIi And hi- specific gravity and thickness, respectively i th layer of soil.
The specific gravity of soils lying below the groundwater level, but above the aquitard, should be taken taking into account the weighing effect of water according to formula (11).
When determining szg in the waterproof layer, the pressure of the water column located above the depth under consideration should be taken into account (see paragraph 3.6).
The lower boundary of the compressible thickness of the base is taken at a depth z= Hc, where the condition is satisfied szр = k× szg(Here szр– additional vertical stress at a vertical depth passing through the center of the foundation base; szg– vertical stress from the soil’s own weight), where k= 0.2 for foundations with b£5m and k= 0.5 for foundations with b> 20 m (at intermediate values k determined by interpolation).
Additional vertical stresses szp,d, kPa, at depth z from the base of the foundation along a vertical line passing through the center of the base of the foundation in question from the pressure along the base of the adjacent foundation are determined by the algebraic summation of stresses szp,cj, kPa, at the corner points of fictitious foundations (Figure 16) according to the formula
With a continuous, uniformly distributed load on the surface of the earth with an intensity q, kPa (for example, from the weight of the leveling embankment) value szp,nf according to formula (36) for any depth z determined by the formula szp,nf = szp + q.
Example 3. Determine the settlement of a free-standing shallow foundation. The engineering geological section is shown in Figure 17. Foundation dimensions: height hf= 3 m; sole b´ l= 3´3.6 m. Pressure along the base of the foundation pII= 173.2 kPa. Soil characteristics:
Layer - gII 1 = 19 kN/m3; E= 9000 kPa;
Layer - gII 2 = 19.6 kN/m3; gs= 26.6 kN/m3; e = 0,661; E= 14000 kPa;
Layer - gII 3 = 19.1 kN/m3; E= 18000 kPa.
Solution. The settlement of a free-standing shallow foundation is determined by formula (31).
Because the foundation depth is less than 5 m, the second term in the formula is not taken into account.
With the width of the foundation base b£ 5 m and the absence of soil layers with E < 5 МПа суммирование проводится до тех пор, пока szр will not become less than 0.2× szg.
The foundation cuts through only one layer of soil - sandy loam (Figure 17), therefore the average calculated value of the specific gravity of the soils lying above the base is also equal to the actual specific gravity of the sandy loam 19 kN/m3.
We find szg, 0 = dn= 19×3.1 = 58.9 kPa; h= l/b= 3.6/3 =1.2; 0.4× b= 0.4×3 = 1.2 m. We divide the base into layers no more than 0.4× thick b. The thickness of the soil layers located under the base of the foundation allows the foundation to be divided into layers 1.2 m thick.
Vertical stresses at depth z from the base of the foundation szp And szу determined by formulas (32) and (33).
Coefficient a we find by interpolation according to table 17, depending on the aspect ratio of the rectangular foundation h and relative depth equal to x=2z/b.
Vertical stress from the soil's own weight szg at the boundary of a layer located at a depth z from the base of the foundation, determined by formula (35).
For silty sand located below the groundwater level, when determining the specific gravity, we take into account the weighing effect of water
The settlement calculations are summarized in Table 18. The parameters that determined the boundary of the compressible strata are shown in bold italics in the bottom line of the table.
The calculation scheme for determining the foundation settlement is shown in Figure 17 (diagram szу not shown in the figure).
Table 18
| No. ige | z, m | x | a | h, m | szp, kPa | szg, kPa | g11, kN/m3 | szg, kPa | 0,2szg, kPa | kPa | kPa | E, kPa | m |
| 1,000 | 173,2 | 58,9 | 58,9 | 11,8 | 114,31 | ||||||||
| 1,2 | 0,8 | 0,824 | 1,2 | 142,7 | 48,53 | 81,7 | 16,3 | 94,19 | 104,3 | 0,0139 | |||
| 2,4 | 1,6 | 0,491 | 1,2 | 84,96 | 28,89 | 104,5 | 20,9 | 56,07 | 75,1 | 0,0100 | |||
| 3,6 | 2,4 | 0,291 | 1,2 | 50,40 | 17,14 | 9,99 | 116,5 | 23,3 | 33,26 | 44,7 | 0,0038 | ||
| 4,8 | 3,2 | 0,185 | 1,2 | 32,04 | 10,9 | 9,99 | 128,5 | 25,7 | 21,15 | 27,2 | 0,0023 | ||
| 0,127 | 1,2 | 21,91 | 7,45 | 9,99 | 140,5 | 28,1 | 14,46 | 17,8 | 0,0015 | ||||
| S | 0,0316 |
The foundation settlement is S= 0.8×0.0316 = 0.025 m.
Determination of stresses in soil masses
Stresses in soil masses that serve as a foundation, medium or material for a structure arise under the influence of external loads and the soil’s own weight.
Main tasks of stress calculation:
Distribution of stresses along the base of foundations and structures, as well as along the surface of interaction of structures with soil masses, often called contact stresses;
Distribution of stresses in the soil mass due to action local load, corresponding to contact stresses;
Distribution of stresses in a soil mass due to the action of its own weight, often called natural pressure.
3.1. Determination of contact stresses along the base of a structure
When foundations and structures interact with soils, foundations appear on the contact surface. contact stress.
The nature of the distribution of contact stresses depends on the rigidity, shape and size of the foundation or structure and on the rigidity (compliance) of the foundation soils.
3.1.1 Classification of foundations and structures by rigidity
There are three cases that reflect the ability of the structure and the foundation to jointly deform:
Absolutely rigid structures, when the deformability of the structure is negligible compared to the deformability of the base and when determining contact stresses the structure can be considered as non-deformable;
Absolutely flexible structures, when the deformability of the structure is so great that it freely follows the deformations of the base;
Structures of finite rigidity, when the deformability of the structure is commensurate with the deformability of the base; in this case, they are deformed together, which causes a redistribution of contact stresses.
A criterion for assessing the rigidity of a structure can be the flexibility indicator according to M. I. Gorbunov-Posadov
Where And - deformation modules of the base soil and structural material; And – length and thickness of the structure.
3.1.2. Model of local elastic deformations and elastic half-space
When determining contact stresses, an important role is played by the choice of the calculation model of the foundation and the method for solving the contact problem. The following foundation models are most widespread in engineering practice:
Model of elastic deformations;
Elastic half-space model.
Model of local elastic deformations.
According to this model, the reactive stress at each point of the contact surface is directly proportional to the settlement of the base surface at the same point, and there is no settlement of the base surface outside the dimensions of the foundation (Fig. 3.1.a.):
Where – proportionality coefficient¸ often called bed coefficient, Pa/m.
Elastic half-space model.
In this case, the soil surface settles both within the loading area and beyond, and the curvature of the deflection depends on the mechanical properties of the soil and the thickness of the compressible thickness at the base (Fig. 3.1.b.):
where is the base stiffness coefficient, – coordinate of the surface point at which the settlement is determined; - coordinate of the force application point ; – integration constant.
3.1.3. The influence of foundation rigidity on the distribution of contact stresses
Theoretically, the diagram of contact stresses under a rigid foundation has a saddle-shaped appearance with infinitely large stress values at the edges. However, due to plastic deformations of the soil, in reality the contact stresses are characterized by a flatter curve and at the edge of the foundation reaches values corresponding to the maximum bearing capacity of the soil (dotted curve in Fig. 3.2.a.)
A change in the flexibility index significantly affects the change in the nature of the contact stress diagram. In Fig. 3.2.b. contact diagrams are presented for the case of a plane problem when the flexibility index t changes from 0 (absolutely rigid foundation) to 5.
3.2. Distribution of stresses in soil foundations due to the soil’s own weight
Vertical stresses from the soil’s own weight at depth z from the surface are determined by the formula:
and the diagram of natural stresses will look like a triangle (Fig. 3.3.a)
In case of heterogeneous bedding with horizontal layers, this diagram will already be limited by the broken line Oabv, where the slope of each segment within the thickness of the layer is determined by the value of the specific gravity of the soil of this layer (Fig. 3.3.b).
Bedding heterogeneity can be caused not only by the presence of layers with different characteristics, but also by the presence of groundwater levels within the soil thickness (WL in Fig. 3.3.c). In this case, one should take into account the decrease in the specific gravity of the soil due to the suspended effect of water on mineral particles:
where is the specific gravity of soil in suspension; - specific gravity of soil particles; - specific gravity of water, taken equal to 10 kN/m3; – coefficient of soil porosity.
3. 3. Determination of stresses in a soil mass due to the action of local load on its surface
The distribution of stresses in the foundation depends on the shape of the foundation in plan. In construction, strip, rectangular and round foundations are most widespread. Thus, the main practical significance is the calculation of stresses for the cases of plane, spatial and axisymmetric problems.
The stresses in the foundation are determined by methods of elasticity theory. In this case, the base is considered as an elastic half-space, endlessly extending in all directions from the horizontal loading surface.
3.3.1. The problem of the action of a vertical concentrated force
The solution to the problem of the action of a vertical concentrated force applied to the surface of an elastic half-space, obtained in 1885 by J. Boussinesq, makes it possible to determine all components of stress and strain at any point in the half-space due to the action of the force (Fig. 3.4.a).
Vertical stresses are determined by the formula:
Using the superposition principle, we can determine the value of the vertical compressive stress at the point under the action of several concentrated forces applied on the surface (Fig. 3.4.b):
In 1892, Flamand obtained a solution for a vertical concentrated force under the conditions of a plane problem (Fig. 3.4.c):
; ; , where (3.8)
Knowing the law of load distribution on the surface within the loading contour, it is possible, by integrating expression (3.6) within this contour, to determine the stress values at any point of the base for the case of axisymmetric and spatial load (Fig. 3.5), and by integrating expression (3.8) - for the case of flat load.
3.3.2. Flat problem. Action of a uniformly distributed load
Scheme for calculating stresses in the foundation in the case of a plane problem under the action of a uniformly distributed load of intensity shown in Fig. 3.6.a.
Exact expressions for determining the stress components at any point in the elastic half-space were obtained by G.V. Kolosov in the form:
where, are influence coefficients depending on dimensionless parameters and ; and – coordinate points at which stresses are determined; – width of the loading strip.
In Fig. 3.7. a-c are shown in the form of isolines, the stress distribution in the soil mass for the case of a flat problem.
In some cases, when analyzing the stressed state of a foundation, it is more convenient to use principal stresses. Then the values of the principal stresses at any point of the elastic half-space under the action of a uniformly distributed strip load can be determined using the formulas of I. H. Mitchell:
where is the visibility angle formed by the rays emanating from a given point to the edges of the loaded strip (Fig. 3.6.b).
3.3.3. Spatial task. Action of a uniformly distributed load
In 1935, A. Love obtained the values of vertical compressive stresses at any point of the base from the action of a load of intensity , evenly distributed over the area of a rectangle of size.
Of practical interest are the stress components related to the vertical drawn through the corner point this rectangle, and acting vertically passing through its center (Fig. 3.8.).
Using influence coefficients we can write:
where - and - are, respectively, influence coefficients for angular and central stresses, depending on the aspect ratio of the loaded rectangle and the relative depth of the point at which the stresses are determined.
There is a certain relationship between the values and.
Then it turns out to be convenient to express formulas (3.11) through the general influence coefficient and write them in the form:
The coefficient depends on dimensionless parameters and: , (when determining the angular stress), (when determining the stress under the center of the rectangle).
3.3.4. Corner point method
The corner point method allows you to determine compressive stresses in the base along a vertical line passing through any point on the surface. There are three possible solutions (Fig. 3.9.).
Let the vertical pass through the point , lying on the contour of the rectangle. Dividing this rectangle into two so that the point M was the angular stress for each of them, the stresses can be represented as the sum of the angular stresses of rectangles I and II, i.e.
If the point lies inside the contour of the rectangle, then it should be divided into four parts so that this point is the corner point for each component rectangle. Then:
Finally, if the point lies outside the contour of the loaded rectangle, then it must be completed so that this point again turns out to be a corner point.
3.3.5. Influence of the shape and area of the foundation in plan
In Fig. 3.10. Diagrams of normal stresses were constructed along the vertical axis passing through the center of the square foundation at (curve 1), strip foundation (curve 2), and also with width (curve 3).
In the case of a spatial problem (curve 1), stresses decay with depth much faster than for a plane problem (curve 2). An increase in the width, and, consequently, the area of the foundation (curve 3) leads to an even slower attenuation of stresses with depth.
It is not possible to determine the actual stress state of foundation soils using modern survey methods. In most cases, they are limited to calculating vertical stresses arising from the weight of the overlying soil layers. The diagram of these stresses along the depth of a homogeneous soil layer will look like a triangle. With layered bedding, the diagram is limited by a broken line, as shown in Fig. 9 (line abсde).
At depth z, the vertical stress will be equal to:
where γ0i is the volumetric weight of the soil of the i-th layer in t/m3; hi is the thickness of the i-th layer in m; n is the number of heterogeneous layers by volumetric weight within the considered depth z. The volumetric weight of permeable soils lying below the groundwater level is taken taking into account the weighing effect of water:
here γу is the specific gravity of solid soil particles in t/m3; ε is the porosity coefficient of natural soil.
With monolithic, practically waterproof clays and loams, in cases where they are underlain by a layer of permeable soil that has groundwater with a piezometric level below the groundwater level of the upper layers, the weighing effect of water is not taken into account. If in the soil bedding shown in Fig. 9, the fourth layer was a monolithic dense clay and in the underlying aquifer the groundwater would have a piezometric level below the groundwater level of the upper layer, then the surface of the clay layer would be an aquifer, receiving pressure from the water layer. In this case, the diagram of vertical stresses would be represented by a broken line abcdmn, as shown in Fig. 9 dotted line.
It should be noted that under the influence of stresses from the own weight of the natural soil, the deformations of the foundation (with the exception of freshly poured embankments) are considered to have long since died out. With a large thickness of water-saturated, highly compressible soils that exhibit creep, sometimes one has to reckon with incomplete filtration consolidation and creep consolidation. In this case, the load from the embankment cannot be considered as the load from the soil’s own weight.
The main condition that must be met when designing foundations is:
where: P - 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 linear 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