The main characteristics of the compressibility of soils are the total deformation modulus E or relative compressibility coefficient, the transverse expansion coefficient (Poisson's ratio) and the lateral pressure coefficient.

1. Relative compressibility factor. When calculating the sediment is often used relative compressibility factor, which is determined by the formula:

We express the expression from the formulas and . We equate the right parts of these expressions, we solve them with respect to mv , we get:

Or mv *p i =s i /h

That. the coefficient of relative compressibility is equal to the relative draft s i/h per unit of effective pressure.

2. Modulus of total deformation E is the coefficient of proportionality between stresses and relative strains. It is determined in the field and laboratory conditions. The most common method is to conduct compression tests with their subsequent processing. In this case, the total deformation modulus will be equal to:

;

Where β - coefficient taking into account the impossibility of lateral expansion of the soil (for sands and sandy loams β = 0.76, loam β = 0.63, clay β = 0,42.

When testing soil with a diameter d stamp according to the results of laboratory tests, E determined by calculation by the formula

E \u003d (1-ν 2) * w * d * ∆p / ∆S

3. Side pressure coefficient ξ is considered as the ratio of the increment of lateral pressure (or ) to the increment of the effective vertical pressure with the obligatory absence of lateral deformations:

According to experimental data, the values ​​of the lateral pressure coefficients vary within the following limits: for sandy soils ξ = 0.25-0.37, clay ξ = 0.11-0.82. Value ξ is determined in triaxial compression devices.

4. Transverse expansion coefficient ν soil (Poisson's ratio) is equal to the ratio of the relative horizontal deformations of the sample ε x to relative vertical εz , i.e..

ORGANIZATION STANDARD

deformation
and strength characteristics
Jurassic clay soils of Moscow

STO 36554501-020-2010

Moscow

Foreword

Standard details:

1 DEVELOPED AND INTRODUCED by the laboratory of electrical technologies (head of the laboratory - candidate of technical sciences Kh.A. Dzhantimirov) NII-OSB im. N.M. Gersevanov - Institute of JSC "NIC "Construction" leading. scientific collaborator, Ph.D. tech. Sciences O.I. Ignatova

3 APPROVED AND INTRODUCED BY Order No. 27 of February 10, 2010, General Director of OAO NITs Stroitelstvo

4 INTRODUCED FOR THE FIRST TIME

Introduction

In connection with the intensive development in recent years in Moscow of high-rise and high-rise buildings with a deep underground part and underground structures, it became necessary to assess the building properties of soils at great depths. These soils include soils of the Jurassic, Cretaceous and Carboniferous periods.

Evaluation of the characteristics of these soils on the basis of statistical generalization of the accumulated archival data of engineering and geological surveys is an urgent task.

To carry out the work, archival materials of laboratory and field tests of pre-Quaternary soils of Moscow were collected from reports on engineering and geological surveys of 40 organizations conducting survey work in the city, which were submitted to the institute for specific design objects.

This standard provides the results of studies for the Jurassic J 3 clay soils.

The results of studies of the relationship between the deformation modulus according to the data of stamp tests and the soil resistivity under the probe cone for the Jurassic clays of Moscow are given in the work, but they were based on little statistical material.

On the basis of the studies carried out for Jurassic clayey soils, tables of standard and calculated values ​​of strength and deformation characteristics were compiled and the coefficients of transition from compression to stamping modules of deformation were established. For these soils, an equation was also obtained for estimating the deformation modulus based on the results of static sounding. The results of the research are published in the work.

These results are recommended to be used in the practice of engineering-geological surveys, design and construction of bases and foundations, which will increase the reliability of deformation and strength characteristics used in base calculations.

ORGANIZATION STANDARD

DEFORMATION AND STRENGTH CHARACTERISTICS JURASSIC CLAY SOILS OF MOSCOW Deformation and strength characteristics of Jurassic clay soils in Moscow

Introduction date 2010-02-25

1 area of ​​use

1.1 This International Standard covers the determination of the deformation and strength characteristics of Jurassic J 3 clay soils of Moscow. These soils were represented by the following deposits: J 3 ν - Volgian stage; J 3 ox- Oxford tier and J 3 cl- Callovian stage. In table. the ranges of variation and average values ​​of the main physical characteristics of the soils of these deposits are given.

1.2 The standard is intended to determine the normative and design values ​​of the deformation and strength characteristics of soils according to tables and equations, depending on their physical characteristics and static sounding data.

1.3 Tables and equations for determining the standard and calculated values ​​of deformation and strength characteristics of soils are recommended to be used for preliminary calculations of foundations and foundations of buildings and structures of the I level of responsibility and final calculations of the bases and foundations of buildings and structures of II and III levels of responsibility.

Index	characteristic values	ρ , t/m 3	e	w L, %	Ip, %	I L	h, m
J 3 ν		1,72	0,48			0,25
		2,14	1,14			0,90
	Average	1,92	0,77			0,29
J 3 ox		1,62	0,82			0,26
		1,93	1,52			0,40
	Average	1,75	1,20			0,04
J 3 cl		1,74	0,60			0,36
		2,04	1,22			0,35
	Average	1,84	0,98			0,06

2 Normative references

Static sounding of soils was carried out with a type II probe in accordance with GOST 19912.

Compression tests of soils were carried out in accordance with GOST 12248 for soils with natural moisture. For research, the results of tests with a finite vertical load were used R≥ 0.5 MPa. The values ​​of compression moduli of deformation were calculated in the range of loads 0.2 - 0.5 MPa.

Values φ And With were determined according to the data of consolidated-drained shear tests of soils of natural moisture in accordance with GOST 12248.

The physical characteristics of soils were determined in accordance with GOST 5180.

3.3 To compile tables of standard and calculated values ​​of deformation and strength characteristics of soils during statistical processing of materials, the apparatus of correlation and regression analysis was used, which makes it possible to establish correlations and regression equations between mechanical characteristics E, φ And With on the one hand, and physical characteristics and static sounding data q with another. The tightness of the connection is characterized by the correlation coefficient R and mean square (standard) deviation S(application ).

The following physical characteristics were used in the correlation analysis: plasticity number I p as an indicator of the type or clay content of the soil; porosity factor e as an indicator of soil density in natural occurrence and an indicator of fluidity I L as an indicator of the state of the soil in terms of consistency.

3.4 Studies of correlations were performed between the standard values ​​of mechanical and physical characteristics and resistance to probing q, defined as the arithmetic mean of particular values ​​for the engineering-geological elements identified during surveys (IGE) (GOST 20522).

To determine the standard and design values E, φ And With according to tables and equations, it is necessary to use the standard values ​​of physical characteristics and resistance to probing q for IGE.

4 Determination of the modulus of deformation from physical characteristics

4.1 Guideline values ​​for the field modulus of deformation E should be taken according to the equation () or table. , compiled on the basis of statistical processing of the results of testing soils with a stamp and a pressuremeter (Fig. ).

Yield rateI L	Standard values ​​of the modulus of deformation E, MPa, with porosity coefficient e equal to
	0,6 - 0,7	0,8 - 0,9	1,0 - 1,1	1,2 - 1,3	1,4 - 1,5
0,25 ≤ I L ≤ 0
0 < I L ≤ 0,25
0,25 < I L ≤ 0,5
0,5 < I L ≤ 0,75

Picture 1- Dependence of the deformation modulus according to die data ( E m) And
pressuremeter ( En) tests ( n IGE = 75; n i= 280) on the coefficient
porosity e and flow rate I L for Jurassic clay soils:
I L:1 - (-0,25); 2 - 0,0; 3 - 0,25; 4 - 0,5; 5 - 0,75

5 Determination of the deformation modulus from static sounding data

5.1 Guideline values ​​for the field modulus of deformation E should be taken depending on the resistivity of the soil under the probe cone q according to the equation (), obtained on the basis of statistical processing of the results of testing soils with a stamp, pressuremeter and static sounding (Fig. ).

Figure 2- Deformation modulus dependence E according to stamp
and pressuremeter tests from soil resistivity
under the probe cone q :
experimental points: 1 - For J3ox; 2 - For J 3 v; 3 - addiction E = f(q)

6 Transition coefficients from compression modulus to stamp modulus

6.1 Conversion factors m k from the compression modulus of deformation to the stamp modulus should be taken or, depending on the porosity coefficient e and flow rate I L(Table ), or depending on the number of plasticity I p and flow rate I L(table).

Yield rateI L	Coefficient valuesm kwith porosity coefficient e equal to
	0,6 - 0,8	0,9 - 1,1	1,2 - 1,5
0,25
0,25
0,75

Yield rateI L	Coefficient valuesm kwith plasticity numberIp equal to
	≤ 7	8 - 17	18 - 30	31 - 50
0,25
0,25
0,75

Figure 3- Coefficient dependency m k from the porosity coefficient e
and flow rate I L for Jurassic clay soils
(n = 32; m k = 2,47 + 0,53e - 1,60I L; R = 0,79; S = 0,42):
I L:

Figure 4- Coefficient dependency m k on the number of plasticity I p
and flow rate I L for Jurassic clay soils
(n = 32; m k = 2,51 + 0,02I p - 1,24I L; R = 0,83; S = 0,38):
I L:1 - (-0,25); 2 - 0,0; 3 - 0,25; 4 - 0,5; 5 - 0,75

When using coefficients m k according to the table and to correct the compression moduli of deformation, the latter should be calculated in the range of vertical pressures of 0.2 - 0.5 MPa, and the values ​​of the coefficient β , taking into account the impossibility of lateral expansion of the soil in the compression device, is 0.4 for clays, 0.62 for loams and 0.72 for sandy loams.

7 Determination of strength characteristics from physical characteristics

7.1 Normative values ​​of the strength characteristics of Jurassic clay soils - the angle of internal friction φ and specific adhesion With obtained from the results of consolidated-drained (CD) soil shear tests should be determined depending on the plasticity number I p and flow rate I L according to the equations () and () or tab. (Fig. and):

Yield rateI L Characteristic designation Standard values φ ° and With, kPa, with plasticity numberI p, %, equal to ≤ 1 8 - 17 18 - 30 31 - 40 41 - 50 0,25 ≤ I L ≤ 0 φ ° With, kPa 0 < I L ≤ 0,25 φ ° With, kPa 0,25 < I L ≤ 0,5 φ ° With, kPa 0,5 < I L ≤ 0,75 φ ° With, kPa 7.2 Design values φ And With should be calculated based on the standard values ​​(Table ), reducing them by the value of the confidence interval Δ, calculated according to the method of adj. 2 SRT with confidence probability α = 0.85 and α = 0.95 (SP 50-101). Confidence interval Δ for φ And With is: Δ φ = 1° Δ With= 7 kPa (at α = 0.85); Δ φ = 2° Δ With= 11 kPa (at α = 0.95). Figure 5- Dependence of the angle of internal friction φ ° from plasticity number I p and flow rate I L Annex A J 3v- Upper Jurassic deposits of the Volgian stage J3ox- Upper Jurassic deposits of the Oxfordian stage J 3cl- Upper Jurassic deposits of the Callovian stage ρ - soil density e- coefficient of soil porosity I p- soil plasticity number I L- index of soil fluidity h- depth of soil sampling or testing with a stamp (pressometer) E w - deformation modulus according to the results of stamp tests E n - deformation modulus according to the results of pressuremeter tests q- soil resistivity under the probe cone during static sounding KD - consolidated-drained soil cut R- correlation coefficient S- standard deviation (standard deviation) Annex B To study the relationship between mechanical at and physical x i characteristics, the apparatus of correlation-regression analysis was used. The calculations were carried out on a computer using a standard program that provides for the construction of a linear dependence of the form To approximate a non-linear dependence, a 2nd or 3rd degree polynomial or equation () is most often used. However, due to the fact that statistical estimates in the theory of correlation are developed only for linear dependencies, non-linear dependencies must be converted to linear ones by changing the variables. m- average number of definitions φ And With in the IGE; n- total number of standard values φ And With(total number of IGE); d 2 - functional characterizing the change in the width of the confidence interval along the dependence. It should be noted that the value d 2 /n at those values n, which took place in the studied sample of experimental data, turned out to be negligible. Estimated values φ And With calculated with confidence probabilities α = 0.85 and α = 0.95, regulated

Lecture plan:

1. General provisions.

2. Deformation properties of soils due to natural conditions.

3. Deformation properties of soils due to external load.

4. Elastic deformations.

5. Factors that determine the elastic properties of soils.

6. Mechanism of plastic deformations.

7. Construction of a compression curve.

8. Deformation indicators.

9. Soil consolidation.

10. Effective and neutral pressure.

11. Method for determining the deformation properties of soils.

1. General Provisions

The mechanical properties of soils are manifested when exposed to external loads.

Mechanical properties are divided into the following types:

- deformation;

- strength;

- rheological.

Deformation properties characterize the behavior of the soil under loads not exceeding the critical ones. That is, they do not lead to the destruction of the soil.

Strength properties characterize the behavior of the soil under loads equal to or greater than the critical ones, and are determined only when the soil is destroyed.

Rheological properties characterize the behavior of the soil under loads over time.

Deformation is the movement of body particles under the action of mechanical stresses.

In regulatory documents, the term soil deformation is used, while these deformations are not associated with external loads, such as swelling deformations, etc.

Therefore, the term deformation properties of soils in practice should be distinguished by the type of impact on the soil:

1. Deformations associated with the impact of natural conditions on the soil.

2. Deformations associated with external loading of the soil.

2. Deformation properties of soils due to natural conditions

swelling deformation evaluated through the index εSW (relative swelling strain). Calculated as follows (Figure 7.1):

ε SW = h h

where h is the initial sample height;

∆h is the increase in the height of the sample during its soaking.

Figure 7.1 - Scheme for calculating the relative deformation of swelling

The nature of swelling - swelling occurs due to the separation of the molecules of the aqueous solution of the structural lattice of crystals.

Settling deformation is estimated through the indicator εS (relative deformation of subsidence) which is calculated as follows (Figure 7.2):

Figure 7.2 - Scheme for calculating the relative deformation of subsidence

The nature of subsidence - when the soil is soaked, structural bonds are destroyed and the soil without load can be deformed.

Frost heave is assessed through the index of relative deformation of frost heaving εfn, which is determined by the formula (Figure 7.3):

				h of − h o

where hof is the frozen ground height;

ho is the initial height of the soil, before freezing.

Figure 7.3 - Scheme for calculating the relative deformation of frost heaving of soils

The nature of frost heaving - with a decrease in temperature< 0 °С вода в порах грунта замерзает и расширяется, что вызывает деформацию грунта.

The above types of soil deformation are associated with natural factors. Below we consider the deformations associated with loading the soil.

3. Deformation properties of soils due to external load - general provisions

A). The concept of stress. b). Types of deformations.

V). Relationship between stress and strain.

A). The concept of stress

To understand this material, consider the concepts of stresses in soils.

External loads transmitted to the ground are mechanical stresses that are a measure of these external forces (figure 7.4). Under mechanical stress is understood the force acting on a unit area of ​​the soil.

Figure 7.4 - Scheme of distribution of external and internal forces acting in the volume of soil at point M

From figure 7.4 it can be seen that three forces (P) act on any point in the soil mass (M). These forces are decomposed into normal (σ) and tangential (τ) stresses. Normal stresses act along the normal to the site, and tangents act along it (Figure 7.5).

		τ yz	τxz
					τzx
				τ yx
		τ zy
			τ yx

Figure 7.5 - Components of shear (τ ij ) and normal (σ i ) stresses

The totality of all stresses for all platforms passing through point M characterizes the stress state at the point. It is determined by the stress tensor (Tσ), the components of which are three normal (σ x, σ y, σ z) and six tangential (τ xy = τ ux, τ yz = τ zy, τ zx = τ xz) stresses.

b). Types of deformations

According to the type of applied load on the ground, the following types of deformations are distinguished:

– linear;

- tangents;

- voluminous.

Linear deformations due to normal stresses (σ). Me-

The swarm of linear deformations is the relative linear deformation (e), which is determined by the formula:

e = h h0

∆h

where h 0 is the initial height of the sample; h is the height of the sample when it is loaded;

∆h is the increment (decrease) in the sample length during its loading.

Tangential deformations due to shear stresses (τ). The measure of tangential strains is the relative shear strain (γ), which is determined by the formula:

γ =
l h 0 o

where h o is the initial height of the sample;

s is the shear value under the influence of shear stresses.

Volume deformations due to the overall load on the body. The measure of volumetric strains is the relative volumetric strain (e v ), which is determined by the formula:

e v = V V

where V is the initial volume of the body;

V1 is the volume of the body obtained under loading;

V is the absolute change in volume under loading.

V = V V − V1

V). Relation between stresses and soil deformations

One of the main issues in soil science (soil mechanics) is to establish a relationship between stresses and strains in soils.

IN In general, this relationship is non-linear and depends on many factors. It is impossible to take into account all the factors, therefore, up to now there is no equation describing these interactions.

IN soil science (soil mechanics) use Hooke's equations.

Hooke's law is written as follows:

– for linear deformationsσ = Е·e , where Е is Young's modulus (modulus of elasticity);

– for tangential deformationsτ = γ·G , where G is the modulus of elasticity of shear;

– for volumetric deformationsσ v = K e V , where K is the bulk modulus.

In practice, when predicting the stability of engineering structures, linear deformations e are most widely used. Tangent and volumetric are used in solving particular problems. Therefore, below we will focus on linear deformations.

Linear deformations

When an external load is applied to the soil, elastic deformations initially occur in it, then plastic and destructive ones (Figure 7.6).

ey

e n e r

Figure 7.6 - Scheme of the formation of elastic (1), plastic (2) and destructive (3) deformations

4. Elastic deformations

Under elastic (volumetric) soil deformations understand the deformation

tions that are restored when the forces that cause them are eliminated (removed) (Figure 7.7).

a) Mechanism of elastic deformation next: when loading the soil, normal and shear stresses arise in it. Normal stresses cause a change in the distance between the atoms of the crystal lattice. Removing the load eliminates the cause caused by a change in the interatomic distance, the atoms return to their original place and the deformation disappears.

If the normal stresses reach the values ​​of the forces of interatomic bonds (the magnitude of the structural bonds in the soil), then the brittle fracture of the soil occurs by separation.

Structure

Figure 7.7 - Scheme of the formation of elastic deformations at the level of: 1 - crystal; 2 - structural connection; 3 - soil

The graphic dependence of stress and soil deformations is shown in Figure 7.8.

	e arr.

Figure 7.8 - Dependence of stresses and deformations of the soil under load OA and unloading AO

Figure 7.8 shows that under loading, the soil is deformed along the OA segment along a linear relationship. When unloading, the soil completely restores its shape, as evidenced by the AO unloading branch, which repeats the OA loading branch.

Hence the deformation e arr. is the elastic part of the total deformation.

b) Measure of elastic deformations is the modulus of elasticity (Young's modulus), which is determined by the dependence (Figure 7.9):

E = σ

e arr.

where σ is stress; e prod. is the relative deformation of the soil.

e prod.

Figure 7.9 - Scheme for determining Young's modulus

The measure of transverse deformations is Poisson's ratio, which is determined by the formula:

μ = e trans.

where e trans - relative transverse deformations.

e trans. =dd

e prod - relative longitudinal deformations.

e prod. = h h

c) Method for determining elastic properties breeds include:

– manufacturing a sample in the form of a cylinder with a height ratio ( h) to diameter (d) equal to 2 ÷ 4;

– loading the sample through a press;

– measurement of longitudinal and transverse deformations at each stage of loading;

– calculation of indicators.

5. Factors determining the elastic properties of soils

The main factors that determine the elastic properties of rocks include:

– fracturing (porosity);

– structural links;

– mineral composition.

Elastic deformations are largely manifested in rocky soils, in dispersed ones they are of subordinate importance. Therefore, we consider the factors that affect the elastic properties of soils, by groups.

Rocky soils

In most rocky soils, the elastic region is preserved up to stresses that are 70–75% of the destructive ones.

Fracturing (porosity)

The influence of fracturing and porosity on the elastic properties of soils is significant. Figure 7.10 shows the dependence of the elastic modulus on porosity.

Figure 7.10 - Dependence of the elastic modulus (E) of soils of different composition on porosity (n):

1 – migmatites and granitoids;

2 - granites;

3 – gabbro and diabase;

4 - labradorites;

5 – ferruginous quartzites;

6 - quartzites and sandstones;

7 – carbonate soils;

8, 9, 10 - basic, medium and acid effusives; 11 - tuffs and tuff brooks.

Figure 7.10 shows that with an increase in porosity from 1 to 20%, the elastic modulus decreases by a factor of 8. A similar pattern is also characteristic of fractured soils (Figure 7.11). With an increase in fracturing, the elastic modulus E decreases by a factor of 3.

Figure 7.11 - Dependence of the dynamic modulus of elasticity (ED) of soils on the degree of tectonic disturbance:

I - weakly fractured;

II - moderately fractured;

III - strongly fractured;

1 - gabbro-dolerites;

2 – porphyritic basalts;

3 – limestones, dolomites, marls;

4 – sandstones, siltstones and mudstones;

5 - pyrrhotite-chalcopyrite ores.

Mineral composition

The elastic parameters are affected quite strongly. Other things being equal, the elastic constants of the soil will be the higher, the higher these constants are for rock-forming minerals.

Structural connections

They are the determining factor, after fracturing, influencing the elastic properties of soils. Yes, in igneous soils, where the cement is the parent rock of the magma, the modulus of elasticity will change from E = 40÷ 160 GPa. IN metamorphic, where the cement is recrystallization parent rock, the values ​​of the modulus of elasticity are lower – Е = 40÷120 GPa. IN sedimentary rocks, where the cement is salts precipitated from infiltration solutions, the modulus value is minimal - E = 0.5 ÷ 80 GPa (Figure 7.12).

Figure 7.12 - The relationship between the material of rigid structural bonds

And modulus of elasticity of rocky soils

At For dispersed soils, the elastic modulus is determined mainly by the type of structural bonds (Figure 7.13). So, in hard clays, with rigid structures,

ties, E = 100 ÷ 7600 MPa, in fluid-plastic, where there is practically no connection, the modulus is E = 2.7 ÷ 60 MPa, i.e. E decreases by 30 ÷ 100 times.

solid (rigid) fluid-plastic (water-caloid)

Figure 7.13 - The relationship between the types of structural bonds and the elastic modulus for clay

The numerical values ​​of some rocky and semi-rocky soils are given in Table 7.1.

Table 7.1 - The values ​​of the characteristics of the elastic properties of rocky and semi-rocky rocks

	Elastic modulus,	Cross-section coefficient
	103 MPa (Jung's)	strain (Poisson)
limestone weak
Sandstone dense
Sandstone weak

1 mPa - 10 kgf/cm2

6. Mechanism of plastic deformations

Plastic deformations are understood as deformations that are not restored when the forces that cause them are eliminated (removed) (Figure 7.14).

In the classical form, plastic deformations in elastic bodies are formed as follows: when a material is loaded, normal and shear stresses arise in it. Under the action of shear stresses, one part of the crystal moves relative to the other. When the load is removed, these displacements remain, i.e., plastic deformation occurs (see Figure 7.14). Normal stresses form elastic deformations.

Figure 7.14 - Scheme of plastic deformation and ductile fracture under the action of shear stresses:

A – unstressed lattice;

b – elastic deformation;

c – elastic and plastic deformation; d – plastic deformation;

e, f - plastic (viscous) fracture as a result of a cut

An elastic body is understood as a material in which there are no pores and cracks. Soils always have pores and cracks. Therefore, the mechanism of formation of plastic deformations is somewhat different from the classical one.

When loading soils, especially dispersed, highly porous ones, normal and shear stresses arise in them. Under the action of normal stresses, elastic deformations (insignificant) are initially formed, then, due to the reduction of pores in the soil, the soil particles move relative to each other. These movements under the action of normal stresses end when the pore space is filled with soil particles. After that, according to the classical scheme, tangential stresses come into play, which form the classical part of plastic deformations.

	σ seal
	∆h1	∆h2
Figure 7.15 - Scheme of the formation of plastic deformations in soils:
a - the initial state of the soil;
b - soil under normal stresses
	compacted (shrank) (σ compacted)
c - soil (particles) under the action of shear stresses
	moved (moved).
Hence the total (total) relative deformation of the soil:

e full. = e total. =			h1 + h2
e szh. =			e s .p . =

Thus, in soils, plastic deformations (e p . ) actually consist of compressive deformations ( e compress. ) and proper plastic e s.p. , i.e.

e p. \u003d e szh. + e s.p. = e total

At the same time, the proportion of proper plastic deformations in the composition of the general ones is insignificant. Therefore, in practice, geologists work with compressive deformation, which we call compressibility.

Compressibility is understood as the ability of soils to decrease in volume (settle) under the influence of external pressure (normal stresses).

7. Building a compression curve

Compressibility indicators are determined in the laboratory under conditions of one-dimensional

noah (linear) problem. Such the type of soil testing, without the possibility of lateral expansion, is called compression, and the device is called an odometer (Figure 7.16).

Figure 7.16 - Scheme of a compression device (odometer) 1 - odometer, 2 - soil, 3 - piston, P - load

When loading the soil in a compression device, the diameter of the sample does not change. Therefore, the relative vertical deformation of the soil is equal to the relative change in volume, i.e.

where h 0 is the initial height of the soil sample;

h is the change in sample height under pressure; V 0 - the initial volume of the soil sample;

V is the change in sample volume under pressure.

Since soil compaction occurs mainly due to a decrease in pore volume, the soil compression deformation is expressed through a change in the value of the porosity coefficient (Figure 7.17).

V = V0 − V1

h = h0

− h

V n = ε 0 V c

Wow yes

=ε 1 V c

water

V 0 = V c (1 + ε 0 )

V c (1+ ε 1 )

Figure 7.17 - Change in the volume of pores in the soil during compression:

A - initial state;

b – after compression;

Vn is the pore volume;

Vs is the volume of the soil skeleton;

ε0 , ε1 – porosity coefficients initial and after compression; h0 is the initial height of the sample;

h is the sample height after compression;

h is the change in sample height under pressure.

Recall that the porosity coefficient is an indicator that characterizes the ratio of the pore volume (V n) to the volume of the mineral part of the soil (V c ).

According to the same scheme, the volume of the sample under loading (V1) is calculated:

V 1 = V c (1 + ε 1 )

Substituting in expression (1) the value of the sample volumes before the experiment and after the experiment (4) and (5), we obtain:

	h = h	V = h		V c (1+ ε 0 ) − V c (1+ ε 1 )	H ε 0 − ε 1
				V c (1+ ε 0 )
	0V0				0 1 + ε 0

From formula (6) we obtain an expression for the soil porosity coefficient corresponding to a given load stage (ε p ):

		εp = ε0			(1+ ε 0 ) = ε 0 − e (1+ ε 0 ),
where e =		is the relative vertical deformation of the soil at a given

pressure P, ε 0 is the initial porosity coefficient.

Knowing the coefficients of porosity (or relative deformations) of the soil at the corresponding load steps, it is possible to construct a compression curve (Figure 7.18).

ε = ρs − ρd

p d

where ρ s is the particle density;

ρ d is the density of dry soil.

ε 1 A

				P, kgf/cm2

Figure 7.18 – Compression curve plotted from porosity factor and load data

8. Indicators characterizing the compressibility of soils

The compressive compressibility of soils can be characterized by different indicators: the compressibility coefficient (a), the modulus of settlement (ep) and the modulus of general deformation (E 0 ).

Compressibility (compression) ratio (a) is defined as follows. For small pressure ranges(1–3 kf/cm 2 ) compression curve between points A and B replace with a straight line, then:

		ε 1 − ε 2
			− P

where ε and P are the measurement intervals for ε and P .

As can be seen from the equation, the compression ratio characterizes the decrease in porosity with an increase in pressure per unit.

Total deformation modulus (E 0 ) also characterizes the decrease in porosity under soil loading and is determined by:

E 0 = β 1 + a ε 0 ,

where ε 0 is the initial coefficient of porosity; a is the compressibility factor;

β - coefficient depending on the transverse expansion of the soil

And approximately equal for sands - 0.8; for sandy loam - 0.7; for loams - 0.5 and for clays - 0.4.

The total deformation modulus can be obtained using Hooke's law:

E = σe

To do this, a compression curve is built according to the relative deformation (e) and load (stress) (Figure 7.19).

e = h h

e 1 e 2

Figure 7.19 - Compression curve built

according to relative vertical deformation (e) and load

The calculation of E 0 is carried out according to the dependence

E 0 =	P2 − P1
	e 1 − e 2

Table 7.1 shows some values ​​of Etot. total deformation modulus.

Table 7.1 - The modulus of the general deformation of various types of rocks according to the results of field experimental tests

		Deformation modulus
		103 MPa	kf/cm2 *
	Krasnoyarsk HPP
Medium fractured granites
Granites are highly fractured
Weathered zone granites	Dneprodzerzhinsk HPP
	Cabril, Portugal
	Canisada, Portugal
	Castelo do Bodie, Portugal
Coarse-grained granites	Salamondi, Portugal
	Bratsk HPP
Weathering zone diabases
	Arges Corben, Romania
Ordovician sandstones	Bratsk HPP
Upper Cretaceous limestones	Chirkeyskaya HPP
Bituminous limestones,	Kasseb, Tunisia
Middle Paleogene
Devonian porphyrites	Talores HPP
Basalts	Bull Run, USA
Tuff lava Quaternary	Zealand
Marl clays of the Tatar stage	Gorkovskaya HPP

* – 1 MPa – 10 kts/cm2

Modulus of settlement (compressibility)

In the practice of calculations, the value of relative vertical deformation is often used directly as a measure of compressibility:

e p = 1000 h h mm / m.

The value e p is called the modulus of settlement and represents the amount of compression in millimeters of a column of soil 1 m high when an additional load P is applied to it.

h is the decrease in sample height at pressure P, mm. h 0 - the initial height of the sample, mm.

Based on the definitions of the modulus of settlement, a curve of dependence of the modulus of settlement on pressure is constructed (Figure 7.20), which allows you to quickly find the amount of settlement of the soil thickness with a thickness of 1 m at a particular pressure.

Modulus of settlement ep in mm/m

	ep = f(Pn)

Vertical pressure Pn , in kg/cm2

Figure 7.20 - Curve of dependence of the modulus of settlement on pressure

9. Consolidation of soils

Compaction of clayey water-saturated soil over time under constant load is called consolidation. Knowledge of the consolidation process

tion of clay soils is necessary for the correct prediction of the rate of settlement of structures.

Consolidation mechanism

In the general case, when an external load is applied to a water-saturated soil, an instantaneous compression initially occurs due to elastic deformations of the pore water and the soil skeleton, then the process of filtration (primary) consolidation begins, due to the squeezing of water from the soil pores, after which the process of secondary soil consolidation occurs, determined by slow displacement of particles relative to each other under conditions of slight squeezing of water from the pores of the soil (Figure 7.21).

Figure 7.22 - General view of the curve of consolidation of water-saturated clay soil (σ z = const):

0-1 - instant compression; 1-2 - filtration (primary) consolidation; 2-3 - secondary consolidation.

Figure 7.22 shows a general view of the consolidation of water-saturated clay soil at σ = const.

One of the parameters of soil consolidation is the coefficient of consolidation (Сv ), which characterizes the speed of the compaction process, determined by the formula:

with v = K f (1+ e ) / aρ in

where Kf is the filtration coefficient;

e – porosity coefficient;

A is the compressibility factor;

ρ in is the density of water; cv is measured in cm2/s.

A high rate of consolidation (large values ​​of cv - about 10-2 ... 10-3 cm2 / s) is typical for coarse (coarse and fine detrital) soils. Sands compact much faster than clays due to their high filtration coefficients. Consolidation of highly dispersed soils proceeds most slowly (low values ​​of cv ≈ 10-5 ... 10-6 cm2 / s), since clays have low filtration coefficients, the squeezing out of bound water in them occurs slowly and with difficulty, causing the so-called long-term or "secular" settlements of structures (Figure 7.23). The duration of such deposits can be several years.

Figure 7.23 - Long-term sedimentation of the silt layer at the base of the Kakhovskaya HPP

1-6 - silts in different parts of the dam

10. The concept of effective and neutral pressures

When predicting the settlement of a soil mass, the magnitude of the external pressure is one of the most important parameters.

In the process of compaction of water saturation of clay soils, not all of the external load is transferred to the soil skeleton, but only part of it, which is called the effective pressure (Pz).

The second part of the loads (Pw) is aimed at squeezing water out of the soil, which is called neutral or pore pressure. Hence the total pressure:

P = Pz + Pw

The concept of effective and neutral pressure is also extended to any normal stress acting in water-saturated soils. In general, you can write:

σ = σ + and

σ = σ − and

i.e., the effective stress σ at any point of the water-saturated soil is equal to the difference between the total σ and the neutral stress.

11. Method of determination

To study the compressibility of soils, a device such as the Terzagi device (Figure 7.24) is currently used, with rigid metal walls that prevent the lateral expansion of the sample when compressed by a vertical load. These are the so-called odometers.

Figure 7.24 - Terzagi Rings

The study of soil resistance to compression is carried out under conditions close to the conditions of soil operation as a result of the construction of the structure.

The load on the device for transferring pressure to the sample is carried out in stages. The first load during standard testing of samples with an undisturbed structure should be equal to the natural load, i.e., the weight of the rock mass overlying the sampling site.

The natural pressure of a homogeneous stratum lying above the groundwater level is calculated by the formula:

ρ ir. \u003d 0.1 N kg / cm2.

The maximum load for soils with undisturbed structure should be 1–2 kg/cm2 more than the sum of the design load from the structure and the pressure of the overlying rock mass.

Each pressure stage imparted to the soil sample is maintained until the deformation is conditionally stabilized. For conditional stabilization of deformation, a compression value is taken that does not exceed 0.01 mm during the time:

– 30 min. - for sandy soils;

– 3 hours - for sandy loam;

– 12 hours - for loams and clays.

The sediment of the sample during the test is determined using a dial indicator with a division value of 0.01 mm, located on the device.

Thus, the deformation properties of soils as a whole can be characterized by the deformation modulus.

In the area of ​​linear compression, the deformation of soils, like any other materials, is characterized by a deformation modulus E and the lateral expansion coefficient ν, called Poisson's ratio. Under the foundations, the lateral expansion of the soil is constrained by the surrounding massif and has little effect on the deformation of the base. The main indicator of deformation should be considered the deformation modulus, which is empirical coefficient in Hooke's formula known from the strength of materials. For homogeneous materials, experimental values E have a small spread and are treated as a constant. The compressibility of soils within a layer (IGE) varies over a wide range. Therefore, their deformation moduli are determined at each construction site according to the results of different types field, laboratory tests, or in terms of physical condition. The test method is selected depending on the level of responsibility of the designed building.

Field trials soils are usually carried out with an inventory stamp, which is a model of the foundation. The equipment used in the field, measuring instruments, the procedure for testing and processing measurement results are described in GOST 20276-99. Stamp 1 (Fig. 3.1) is installed in a pit or mine working, tightly rubbed against the surface of the soil mass and loaded with individual load stages by a hydraulic jack 3 resting against an anchor beam 5 connected to blocks 4, or piece weights. Load steps are taken depending on the type and condition of the soil and are maintained until stabilization of the subsidence of the base. Settlement is measured by deflection meters or, more conveniently, by indicators 7 fixed on a fixed base 8. The design of the installations for loading the stamp and the scheme for measuring the settling may be different. Based on the test results, a graph is built (Fig. 3.2), on the horizontal axis of which the pressures are indicated, and the measured precipitation of the stamp is plotted along the vertical axis. An empirical curve constructed from experimental points often represents a broken line, which in a certain pressure range ∆р, allowing a small error, is replaced by an average straight line constructed by the least squares method or a graphical method. For initial values p g and s 0 (the first point included in the averaging) take the pressure from the own weight of the soil at the depth of the stamp, and the corresponding draft; and for final values r to And s to- pressure and draft values ​​corresponding to a point on a straight section of the graph. The number of points included in the averaging must be at least three. Soil deformation modulus E calculated for the linear section of the graph by the formula

(3.1)

Where v- Poisson's ratio, taken equal to 0.27 for coarse soils; 0.30 - for sands and sandy loams; 0.35 - for loams; 0.42 - for clays;

TO 1 - coefficient taken equal to 0.79 for a rigid round stamp;

D- die diameter.

The remaining designations are shown in Fig. 3.2.

According to the design standards SNiP 2.02.01-83*, the number of experiments for each selected engineering-geological element should be at least 3. Soil deformation moduli calculated by formula (3.1) are the most reliable. The disadvantage of the method is that the cost of testing dies is relatively high.

Laboratory tests. Under laboratory conditions, soil samples are tested in devices that usually exclude lateral expansion. This test method is called compressive compression, and the design of devices for testing by compression devices or odometers. The odometer device is shown in Figure 3.3, the test procedure is set out in GOST 12248-96. The test soil sample 11, enclosed in the working ring 3, is installed in the device on a perforated insert 6. A perforated metal stamp 5 is placed on top of it, designed for uniform distribution of force N transmitted to the sample using a special loading device. Under the action of pressure, which increases in steps of 0.0125 MPa or more, the stamp settles due to sample compression. Its movement, which continues for quite a long time, is measured by two indicators 8 with an accuracy of 0.01 mm. When the sample is compressed, the pore volume of the soil decreases and water is squeezed out of them, which is discharged through the holes in the stamp and the liner.

Soil compaction is usually characterized by a decrease in the porosity coefficient. The initial value of the coefficient of porosity e about is determined by the formula given in table. 1.3. At each load stage, the porosity coefficient is calculated by the formula

e i \u003d e 0 -(1+e 0) (3.2)

Where s i- the value of the measured displacement (settlement) of the stamp at pressure p i;

h is the height of the soil sample.

Changes in the coefficient depending on the pressure are shown in fig. 3.4. The experimental points on the graph are connected by straight lines. The constructed empirical dependence in the general case represents a broken line, which is usually called compression curve. For pressure range from r n before r to, taken from the same considerations as for stamp tests, the section of the compression curve is replaced by a straight line. Such a replacement allows us to calculate the deformability parameter, called the compressibility factor T 0:

t 0 = (3.3)

The meaning of the compressibility coefficient is the tangent of the angle of inclination of the averaged straight line to the horizontal axis.

The deformation modulus is determined by the compressibility factor from the expression:

E to = (3.4)

Where β – coefficient depending on the coefficient of lateral expansion ν is calculated by the formula

Where v- coefficient of transverse deformation, taken equal to: 0.30-0.35 - for sands and sandy loams; 0.35-0.37 - for loams; 0.2¾0.3 at I L < 0; 0,3¾0,38 при 0 £ I L£0.25; 0.38¾0.45 at 0.25< I L£ 1.0 - for clays (smaller values v taken at a higher density of the soil).

Since the soils are heterogeneous, the deformation moduli of the soil layers are found as the average of the results of at least 6 experiments.

For a number of reasons, the magnitude E to turn out to be significantly underestimated. For buildings of I and II levels of responsibility, the values ​​of the deformation modulus, established by the results of compression tests, are determined by the formula

E \u003d t to E to (3.6)

Empirical coefficient t to found by comparing field tests of stamps with laboratory tests.

t to = (3.7)

Values t to for soils of different types and conditions vary over a wide range. Their approximate values ​​in practice are taken from Table. 5.1 of the set of rules for the design and installation of foundations SP 50-101-1004, or according to tables compiled for the soil conditions of individual regions.

Soil samples can be tested in the laboratory using a more complex triaxial compression scheme. The test procedure is set out in GOST 12248-96. Such tests make it possible to establish not only the modulus of deformation, but also the strength characteristics described in Chap. 5. In practice, triaxial tests are not widely used. Difficulties in their implementation increase, and the obtained values ​​of the modulus of deformation must be corrected, as in compression tests.

A lot of data on natural soils makes it possible to obtain tests by static sounding in accordance with GOST 19912-2001. Modern probes consist of a friction sleeve and a tip (cone). Probing is carried out by pressing the probe into the soil mass with simultaneous measurement continuously or through 0.2 m of resistance fs And q c(Fig. 3.5), which can be recorded on a magnetic disk and processed on a computer. Together with drilling and other types of tests, static sounding makes it possible to solve many problems more reliably. These include the following questions:

allocation of engineering-geological elements (IGE) and the establishment of their boundaries;

assessment of the spatial variability of the composition and properties of soils;

quantitative assessment of the characteristics of the physical and mechanical properties of soils.

A quantitative assessment of the modulus of deformation and other indicators of the physical and mechanical properties of soils is made on the basis of reasonable statistical dependencies between them and indicators of soil resistance to the penetration of the probe. Usually a dependency of the form is used E=f(q c). It is advisable to set the parameters of such a dependence for regional types of soils. If available, static sounding can significantly reduce the cost of soil testing.

To find the modulus of deformation, the opening continues to be used, based on its relationship with indicators of the physical state. The connection is probabilistic. However, tables were compiled on its basis, from which the deformation modulus is taken for clay soils of various origins in terms of fluidity I L and porosity coefficient e. For loose soils, the deformation modulus is taken from the particle size distribution and porosity coefficient e. The tables are given in design standards, codes of practice, in reference books, and are advisory in nature. They can only be used for preliminary calculations.

Questions for self-examination.

1 What indicators characterize the deformation of soils in the area of ​​linear compression?

2. What does the soil deformation modulus mean?

3. What tests are carried out to determine the modulus of deformation?

4. How many tests of dies are necessary to determine the deformation modulus of a homogeneous layer (IGE)?

5. How many compression tests should be carried out to determine the EGE deformation modulus?

6. How are the results of soil compression tests corrected?

7. The essence of static sounding of soils.

8. Is it possible to take the modulus of soil deformation in terms of physical condition?

THEME 4

Foundation settlement calculation.

The calculation of foundation settlement in engineering practice is based on Hooke's solution for determining the shortening or stretching of an elastic rod loaded with an axial force.

When force is applied N rod shortening (Fig. 4.1 A), as follows from Hooke's theory, is calculated from the expression

s = N L / A E.

If we accept that σ=N / ​​A(A- cross-sectional area of ​​the rod) , That

s = σ L / E. (4.1)

Work σL in this formula has a simple geometric meaning, meaning, in fact, the area of ​​a rectangular stress diagram.

By analogy with the core of the foundation sediment s(Fig. 4.1 b) is understood as a shortening of some soil conditionally identified under the sole of a column of soil with a height Nose. Calculating its magnitude s according to formula (4.1) is complicated by the following circumstances: stresses σz they are unevenly distributed over horizontal sections and along the height of the column (the stress diagrams along them are curvilinear); post height Nose, since it cannot be measured, it must be found in some way; within Nose there may be layers of different compressibility. The listed problems are approximately solved in the engineering calculation of settlement by the layer-by-layer summation method.

The essence of the method is that the sediment of the base s is calculated on the basis of formula (4.1) as the sum of the deformations of sections that are homogeneous in compressibility, into which the soil mass is divided from the base to the lower boundary of the compressible thickness. This technique is similar to the well-known method for approximately determining the areas of curvilinear figures.

The calculation is made in the following sequence.

Determine the pressure at the level of the base of the foundations from the own weight of the soil:

σzg= g 1 d 1 (4.2)

Determine the additional pressure from the load on the foundation that has arisen under the sole in excess of the pressure from the own weight of the soil:

p o = r n –σzg (4.3)

The soil massif under the sole is conditionally divided into sections of uniform compressibility (Fig. 4.2) with a thickness h i£ 0.4b. If within the elementary section there is a boundary between the soil layers, then the site is divided into two parts along it (in the figure, point 2 is taken on the border between EGE 1 and EGE 2).

At points on the boundaries of the sections, additional stresses are calculated

σzi = a p o, (4.4)

where a is the coefficient taken according to Table. 2.3 depending on the aspect ratio of the sole h =l/b and the relative depth of the point ξ =2z i /b (z i is the distance from the base of the foundation to the considered point, i- point number), and stress from the own weight of the soil

σ zqi = σzg+∑h i g i. (4.5)

Find the position of the boundary of the compacted stratum by checking the empirical condition

σzi ≈ k σ zqi, (4.6)

Where k=0.2 at deformation modulus E≥5 MPa, and k=0.1 at E< 5 MPa.

The discrepancy between the right and left parts of the condition is allowed no more than 5 kPa.

Based on the stress values ​​calculated at the points, a stress diagram is built (Fig. 4.3) and average pressures are calculated σz with i for all areas within the compressible thickness

σz with i = (σz(i-1) +σzi)/2, (4.7)

Where σz(i-1) And σzi– pressure at the upper and lower boundaries i-th site.

Calculate the settlement of the foundation as the sum of deformations of elementary sections ranging from the sole to the boundary of the compressible thickness

s= 0.8å σ z c i h i / E i. (4.8)

In this formula, the sum of the products å σ z c i h i means the approximate area of ​​the curvilinear stress diagram.

The initial data on the depth of laying and the dimensions of the base of the foundations necessary for performing the calculations are indicated in Table. 4.1.

Table 4.1

Foundation Data	Variant number
Depth d1 , m	1.5	2.8	2.1	2.4	1.8		2.5	3.3		2.9	2.3	3.1	2.2
Pressure, kPa
width b m	1.6	2.4	2.1	2.7	1.8	1.5	2.3	1.6	1.9	2.2	2.9		3.2
length l, m	2.4		2.7	3.3	2.4	2.1	3.4		3.2	2.8	4.1	4.5	4.2
Width b m	1.6	2.4	2.1	2.7	1.8	1.5	2.3	1.6	1.9	2.2	2.9		3.2
Foundation Data	Variant number
Depth d1 , m	3.1	2.2	2.5	3.3		2.9	2.3	3.1	2.2	1.5	2.8	2.1	2.4
Pressure, kPa
Dimensions of the sole of a separate foundation, m
width b m	2.5	3.3		2.9	1.5	2.8	2.1	2.3	3.1	2.2	2.7	1.8	1.5
length l, m	3.3	4.2	2.4	3,6	2.7	3.3	2.4		4.5	4.5	4.1	1.8	2.1
Strip footing dimensions
Width b m	2.5	3.3		2.9	1.5	2.8	2.1	2.3	3.1	2.2	2.7	1.8	1.5

Occurrence, numbers of soil layers (IGE), values ​​of IGE indicators are taken for a given variant according to fig. 1, tab. 1 and table 2.

The pressures on the ground indicated in Table 4.1 refer to separate and strip foundations.

When studying a topic on your own, perform settlement calculations for separate and strip foundations.

Example 4.1.

b = 1.8 m, l = 2.5 m, d 1 = 1.8 m, p n = 240 kPa. Information about soils is given in Figure 4.3.

Household pressure at the foundation level

σzg= g 1 d 1= 19*1,8 = 34.2 kPa.

Additional pressure under the base of the foundation

p o = r n –σzg = 240 - 34.2 = 205.8 kPa.

Elementary layer thickness

h=0.4b=0,4 *1.8 = 0.72 m.

The ratio of the sides of the base of the foundation

h = l / b \u003d 2.5 / 1.8 \u003d 1.39 ≈ 1.4.

1st point (i = 1), z 1 \u003d 0.72 m;

x=2z 1 /b = 2*0.72 /1.8 = 0.8, a= 0.848;

σz 1=a p o = 0.848 *205.8 = 174.5 kPa.

σ z с1 = (205.8 + 174.5) / 2 = 190.15 kPa;

Stress from the own weight of the soil

σzq 1 = σzg+h 1 g 1.= 34,2 + 0,72 *19 = 47.88 kPa.

2nd point(i = 2). If this point is taken 0.72 m lower, it will be in the 2nd layer. Since the area must be uniform in compressibility, the point should be located on the boundary between the layers. Therefore, the distance from the sole to the point will be z 2 \u003d 1.05 m, and the thickness of the second section will be

h 2 = 1.05 - 072 = 0.33 m:

x = 2 *1,05 / 1,8 = 1,17 , a=0.694,

σz 2= 0,694 *205.8 = 142.8 kPa,

σ z с2 = (174.5 + 142.8)/2=158.6 kPa,

σzq 2 = 47,88 + 0,33 *19 = 54.15 kPa.

3rd point(i = 3). For the convenience of using the table, in order to avoid interpolation when finding the values ​​​​a from it, we will take z 3 \u003d 1.44 m. The thickness of the third section will be h 3 =1.44 - 1.05 = 0.39 m.

x \u003d 2 * 1.44 / 1.8 \u003d 1.6; a=0.532;

σz 3 = 0,532 *205.8 = 109.5 kPa;

σ z c3 \u003d (142.8 + 109.5) / 2 \u003d 126.1 kPa;

σzq 3 =54.15+0.39*20.3 = 62.1 kPa.

4th point(i = 4). Section thickness 0.72 m, z = 2.16 m.

x = 2 *2,16 / 1,8 = 2,4 ; a=0.325;

σz 4= 0.325*205,8 = 66.9 kPa;

σ z c4 \u003d (109.5 + 66.9) / 2 \u003d 88.2;

σzq 4 = 62.1+ 0.72*20.3 = 76.7 kPa.

For points below, the stresses are calculated in a similar way. The results of all calculations performed are given in Table. 4.2.

At the 7th point, the left and right parts of the condition σ zi ≈0.2σ zqi (marked in gray in the table) differ by 2.39 kPa, less than 5 kPa. Therefore, the boundary of the compacted zone can be taken at this point at a depth of 4.32 m from the base of the foundation. Soils within this depth are the base.

Table 4.2

Point number	Layer number	Z V m	h i V m	x=2 z/b	a	σzi in kPa	σ zс i in kPa	σzq in kPa	0,2σzq in kPa
					1,000	205,8		34,2	-
	0,72	0,72	0,8	0,848	174,5	190,1	47,88	9,6
	1,05	0,33	1,17	0,694	142,8	158,6	54,15	10,83
		1,44	0,39	1,6	0,532	109,5	126,1	62,1	12,42
	2,16	0,72	2,4	0,325	66,9	88,2	76,7	15,34
	2,88	0,72	3,2	0,21	43,22	55,06	91,3	18,26
	3,6	0,72	4,0	0,145	29,8	36,51	105,9	21,18
		4,32	0,72	4,8	0,105	21,61	25,7	120,0	24,0

The draft is

ѕ= 0,8[(190,1 *0,72+158,6 *0,33)/7200+(126,1 *0,39+88,2 *0,72+55,06 *0,72+36,51 *0,72)/12000 ++25,7 *0,72/16000] = 0.034 m.=3.4 cm.

The settlement of the strip foundation is calculated in the same sequence. With the same pressure on the ground and the same width of the sole, the calculated settlements turn out to be different. To find out the reason for this compare stress diagrams.

Conclusion.

It should not be overlooked that the soil column allocated under the foundations is a foundation model, the deformations of which are established on the basis of hypotheses about the distribution of stresses in the soil mass, the location of the boundary of the deformable zone, and the compressibility of soils. Due to the accepted simplifications, the model parameters used in the calculations differ from the parameters of the real soil. As a result, the calculated settlements in practice usually do not coincide with the actual foundation settlements. Settling calculations using the layered summation method are therefore approximate.

The layer-by-layer summation method, using the method of corner points for determining stresses, can be used to determine the settlement of adjacent foundations.

It should be noted that foundation settlements do not occur immediately after the load is applied, but slowly increase with time. The duration of soil deformation can be approximately calculated or taken from observations.

Questions for self-examination.

1. What decision is taken as the basis for calculating the draft?

2. What difficulties arise when calculating the settlement of foundations?

3. In what sequence is the settlement calculated?

4. How is the position of the boundary of the compacted zone determined?

5. How is the different compressibility of the foundation soils taken into account?

6. What is the reliability of the layered summation method?